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Chapter 5: Growth-Adjusted
1
Seasonal Factors Model
Original
Data
Equated Day
Factors
Holiday
Factors
Normalized
Data
Initial
Seasonal
Factors
Seasonally-
Adjusted
Data:
Initial
Seasonally-
Adjusted
Data:
Initial
Growth Rate
(Adjustments)
Events
(Adjustments)
Seasonally-
Adjusted
Data:
Final
Growth-Adj
Seasonal
Factors
Growth-Adjusted Seasonal Factors Model
2
This chapter will walk through the model structure that will be used to arrive
at the growth-adjusted seasonal factors.
1. Introduction
2. Inputs
3. Calc
4. Trend
1. Introduction – why growth-adjust?
2. Model Structure: Inputs
3. Model Structure: Calc
4. Model Structure: Trend
Introduction
Growth-Adjusted Seasonal Factors Model
Jan
Jan
Dec
Jan
Dec
Dec
Dec is much higher
than Jan each year
due to GROWTH,
not to seasonality.
XYZ Sales – with Growth
WITH
Growth
Year 1 Year 2 Year 3
3
Growth is removed so the seasonality measure only captures seasonality,
nothing else.
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
Jan
Dec
Dec is much higher
than Jan each year
due to GROWTH, not
to seasonality.
XYZ Sales – with & without Growth
WITH
Growth
WITHOUT
Growth
Without Growth,
the “true”
seasonal pattern is
more obvious.
Year 1 Year 2 Year 3
Jan
Dec
4
Removing growth reveals the “true” relationship between January and
December (& all other months).
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
Sep
Year 1 Year 2 Year 3
Seasonal pattern
can be further
skewed if Events
are included.
XYZ Sales – with & without Growth & Events
WITH
Growth
& Event
WITHOUT
Growth
&
Event
Adjusting for
Events as well as
Growth reveals
seasonal pattern.
New
product lifts
sales in Sep
by 15%
WITH
Growth
only
5
Adjustments need to be made for events as well.
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
6
After adjusting for growth & events, the “true” underlying seasonal pattern
emerges.
1. Introduction
2. Inputs
3. Calc
4. Trend
Seasonality:
Without Growth Adjustment
Seasonality:
With Growth Adjustment
Growth-Adjusted Seasonal Factors Model
7
The Excel model for developing the growth-adjusted seasonal factors, and for
estimating trend, has three parts.
1. Data Inputs (“Inputs” tab)
2. Calculations (“Calc” tab)
3. Trend Estimate (“Trend” tab)
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
8
The “Inputs” tab contains all the key information drawn from other files that
will be used to estimate trend.
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A B C D E F
Key Inputs
Linked to diff file
Actuals
No. of
Days
Norm
Factor
Normalized
Data
Jan-01 27.844 21.7 1.05 26.510
Feb-01 21.631 19.1 0.92 23.459
Mar-01 27.970 22.0 1.07 26.229
Apr-01 25.529 19.7 0.95 26.799
May-01 24.568 21.9 1.06 23.175
Jun-01 24.674 21.0 1.02 24.284
Jul-01 23.878 19.8 0.96 24.883
Aug-01 23.591 22.8 1.10 21.354
Sep-01 25.417 15.0 0.72 35.098
Oct-01 30.229 22.6 1.09 27.692
Nov-01 26.672 20.4 0.99 27.054
Dec-01 25.506 17.8 0.86 29.529
Jan-02 29.943 21.3 1.03 29.056
Feb-02 26.255 19.1 0.92 28.474Jan-16 29.393 19.5 0.94 31.219Feb-16 29.857 20.0 0.97 30.918Mar-16 29.947 21.8 1.06 28.373Apr-16 26.183 21.0 1.02 25.739May-16 25.757 20.8 1.01 25.606Jun-16 30.123 22.0 1.06 28.334
Jul-16 22.328 19.9 0.96 23.217
Aug-16 23.490 23.0 1.11 21.141
Sep-16 25.282 20.8 1.01 25.100
Oct-16 22.795 20.5 0.99 22.964
Nov-16 22.000 20.4 0.99 22.307
Dec-16 22.000 19.0 0.92 23.878
Jan-17 0.000 20.4 0.99 0.000
Feb-17 0.000 19.0 0.92 0.000Jan-20 0.000 21.4 1.03 0.000Feb-20 0.000 19.0 0.92 0.000Mar-20 0.000 21.9 1.06 0.000Apr-20 0.000 20.8 1.01 0.000May-20 0.000 19.8 0.96 0.000Jun-20 0.000 21.9 1.06 0.000Jul-20 0.000 22.0 1.07 0.000Aug-20 0.000 20.9 1.01 0.000Sep-20 0.000 20.8 1.01 0.000Oct-20 0.000 21.6 1.05 0.000
Nov-20 0.000 19.3 0.93 0.000
Dec-20 0.000 19.3 0.94 0.000
Jan-21 0.000 0.0 0.00 0.000
TrendModel: Inputs
Update with
data thru Dec
2016
1. Introduction
2. Inputs
3. Calc
4. Trend
Model Structure: Inputs
Growth-Adjusted Seasonal Factors Model
9
The “Inputs” tab also brings in the seasonal factors – the initial factors already
developed, and the growth-adjusted factors to be developed in the model.
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A B C D E F G H I J
Key Inputs
Linked to diff file
Actuals
No. of
Days
Norm
Factor
Normalized
Data None Initial
Growth-
Adjusted
Jan-01 27.844 21.7 1.05 26.510 1.00 1.00 1.03
Feb-01 21.631 19.1 0.92 23.459 1.00 0.96 0.98
Mar-01 27.970 22.0 1.07 26.229 1.00 1.00 1.01
Apr-01 25.529 19.7 0.95 26.799 1.00 0.99 1.01
May-01 24.568 21.9 1.06 23.175 1.00 0.99 1.00
Jun-01 24.674 21.0 1.02 24.284 1.00 1.02 1.03
Jul-01 23.878 19.8 0.96 24.883 1.00 0.98 0.97
Aug-01 23.591 22.8 1.10 21.354 1.00 0.93 0.89
Sep-01 25.417 15.0 0.72 35.098 1.00 1.00 1.01
Oct-01 30.229 22.6 1.09 27.692 1.00 1.02 1.02
Nov-01 26.672 20.4 0.99 27.054 1.00 1.03 1.00
Dec-01 25.506 17.8 0.86 29.529 1.00 1.07 1.06
Jan-02 29.943 21.3 1.03 29.056
Feb-02 26.255 19.1 0.92 28.474Jan-16 29.393 19.5 0.94 31.219Feb-16 29.857 20.0 0.97 30.918Mar-16 29.947 21.8 1.06 28.373Apr-16 26.183 21.0 1.02 25.739May-16 25.757 20.8 1.01 25.606Jun-16 30.123 22.0 1.06 28.334
Jul-16 22.328 19.9 0.96 23.217
Aug-16 23.490 23.0 1.11 21.141
Sep-16 25.282 20.8 1.01 25.100
Oct-16 22.795 20.5 0.99 22.964
Nov-16 22.000 20.4 0.99 22.307
Dec-16 22.000 19.0 0.92 23.878
Jan-17 0.000 20.4 0.99 0.000
Feb-17 0.000 19.0 0.92 0.000Jan-20 0.000 21.4 1.03 0.000Feb-20 0.000 19.0 0.92 0.000Mar-20 0.000 21.9 1.06 0.000Apr-20 0.000 20.8 1.01 0.000May-20 0.000 19.8 0.96 0.000Jun-20 0.000 21.9 1.06 0.000Jul-20 0.000 22.0 1.07 0.000Aug-20 0.000 20.9 1.01 0.000Sep-20 0.000 20.8 1.01 0.000Oct-20 0.000 21.6 1.05 0.000
Nov-20 0.000 19.3 0.93 0.000
Dec-20 0.000 19.3 0.94 0.000
Jan-21 0.000 0.0 0.00 0.000
Seasonal Factors
TrendModel: Inputs
Update with
data thru Dec
2016
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
10
The “Calc” tab is where all the calculations are performed. Except for
updating monthly data, this tab need never be touched.
TrendModel: Calc
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A B C D E F G H I J K L M N O P Q R S T U
Calculations Unit: 1
In Use (1 = None; 2 = Initial; 3 = Final) : 2 Start: 25.000
Actuals
Adjust-
ments
Adjusted
Actuals
Normalization
Factors
Normalized
Data None Initial Revised In Use
Seasonally-
Adjusted:
Monthly
Seasonally-
Adjusted: 3-
Mo Avg
Growth
Rate
1-Time
Events
Estimated
Trend
Estimated
Trend
Values
Extrapolated
Trend
Extrapolated
Trend Values
(= Forecast)
Estimated (&
Forecast)
Trend
Actual (&
Forecast)
Values
Estimate vs
Actual: Diff
Jan-01 27.844 27.844 1.05 26.510 1.00 1.00 1.03 1.00 26.406 25.412 2.0% 0.0% 25.000 26.362 25.000 27.844 (2.844)
Feb-01 21.631 21.631 0.92 23.459 1.00 0.96 0.97 0.96 24.418 25.666 2.0% 0.0% 25.042 22.184 25.042 21.631 3.411
Mar-01 27.970 27.970 1.07 26.229 1.00 1.00 1.01 1.00 26.174 25.849 2.0% 0.0% 25.083 26.805 25.083 27.970 (2.887)
Apr-01 25.529 25.529 0.95 26.799 1.00 0.99 1.01 0.99 26.954 25.517 2.0% 0.0% 25.125 23.797 25.125 25.529 (0.404)
May-01 24.568 24.568 1.06 23.175 1.00 0.99 1.00 0.99 23.424 24.712 2.0% 0.0% 25.167 26.397 25.167 24.568 0.599
Jun-01 24.674 24.674 1.02 24.284 1.00 1.02 1.02 1.02 23.756 24.153 2.0% 0.0% 25.209 26.183 25.209 24.674 0.535
Jul-01 23.878 23.878 0.96 24.883 1.00 0.98 0.97 0.98 25.279 24.015 2.0% 0.0% 25.251 23.852 25.251 23.878 1.373
Aug-01 23.591 23.591 1.10 21.354 1.00 0.93 0.89 0.93 23.011 27.767 2.0% 0.0% 25.293 25.930 25.293 23.591 1.702
Sep-01 25.417 25.417 0.72 35.098 1.00 1.00 1.01 1.00 35.011 28.406 2.0% 30.0% 32.936 23.911 32.936 25.417 7.519
Oct-01 30.229 30.229 1.09 27.692 1.00 1.02 1.02 1.02 27.195 29.510 2.0% -20.0% 26.393 29.337 26.393 30.229 (3.836)
Nov-01 26.672 26.672 0.99 27.054 1.00 1.03 1.00 1.03 26.326 27.069 2.0% 0.0% 26.437 26.784 26.437 26.672 (0.235)
Dec-01 25.506 25.506 0.86 29.529 1.00 1.07 1.07 1.07 27.685 27.651 2.0% 0.0% 26.481 24.396 26.481 25.506 0.975
Jan-02 29.943 29.943 1.03 29.056 1.00 1.00 1.03 1.00 28.941 28.754 2.0% 0.0% 26.525 27.443 26.525 29.943 (3.418)Feb-02 26.255 26.255 0.92 28.474 1.00 0.96 0.97 0.96 29.637 28.775 2.0% 0.0% 26.569 23.537 26.569 26.255 0.314Mar-02 26.743 26.743 0.96 27.806 1.00 1.00 1.01 1.00 27.747 28.260 2.0% 0.0% 26.613 25.650 26.613 26.743 (0.130)Apr-02 28.761 28.761 1.06 27.239 1.00 0.99 1.01 0.99 27.397 27.017 2.0% 0.0% 26.658 27.985 26.658 28.761 (2.103)May-02 27.152 27.152 1.06 25.632 1.00 0.99 1.00 0.99 25.908 28.461 2.0% 0.0% 26.702 27.984 26.702 27.152 (0.450)Jun-02 31.740 31.740 0.97 32.791 1.00 1.02 1.02 1.02 32.079 33.049 2.0% 0.0% 26.747 26.464 26.747 31.740 (4.993)Jul-02 41.499 41.499 1.02 40.516 1.00 0.98 0.97 0.98 41.160 34.472 1.0% 0.0% 26.769 26.989 26.769 41.499 (14.730)Aug-02 29.511 29.511 1.05 28.003 1.00 0.93 0.89 0.93 30.177 33.477 1.0% 0.0% 26.791 26.200 26.791 29.511 (2.719)Sep-02 28.180 28.180 0.97 29.168 1.00 1.00 1.01 1.00 29.095 31.102 1.0% 0.0% 26.813 25.971 26.813 28.180 (1.367)Oct-02 38.061 38.061 1.10 34.657 1.00 1.02 1.02 1.02 34.034 31.178 1.0% 0.0% 26.836 30.011 26.836 38.061 (11.225)Nov-02 29.087 29.087 0.93 31.245 1.00 1.03 1.00 1.03 30.404 30.700 1.0% 0.0% 26.858 25.695 26.858 29.087 (2.229)Dec-02 26.205 26.205 0.89 29.503 1.00 1.07 1.07 1.07 27.660 29.293 1.0% 0.0% 26.881 25.466 26.881 26.205 0.676
Jul-16 22.328 22.328 0.96 23.217 1.00 0.98 0.97 0.98 23.585 24.695 1.0% 0.0% 30.790 29.149 30.790 22.328 6.821
Aug-16 23.490 23.490 1.11 21.141 1.00 0.93 0.89 0.93 22.782 23.801 1.0% 0.0% 30.815 31.773 30.815 23.490 8.283
Sep-16 25.282 25.282 1.01 25.100 1.00 1.00 1.01 1.00 25.037 23.457 1.0% 0.0% 30.841 31.143 30.841 25.282 5.861
Oct-16 22.795 22.795 0.99 22.964 1.00 1.02 1.02 1.02 22.552 24.850 1.0% 0.0% 30.867 31.200 30.867 22.795 8.405
Nov-16 27.327 27.327 0.99 27.708 1.00 1.03 1.00 1.03 26.963 24.306 1.0% 0.0% 30.892 31.310 30.892 27.327 3.983
Dec-16 23.000 23.000 0.92 24.963 1.00 1.07 1.07 1.07 23.404 25.183 1.0% 0.0% 30.918 30.385 30.918 23.000 7.385
Jan-17 0 0 0.99 0 1.00 1.00 1.03 1.00 1.0% 0.0% 30.944 30.666 30.944 30.666 0
Feb-17 0 0 0.92 0 1.00 0.96 0.97 0.96 1.0% 0.0% 30.970 27.396 30.970 27.396 0
Mar-17 0 0 1.12 0 1.00 1.00 1.01 1.00 1.0% 0.0% 30.996 34.673 30.996 34.673 0
E. Estimate & Actual
Seasonal Factors
A. Actual & Normalized Data B. Seasonally-Adjusted Data C. Estimated Trend D. Forecasts
1. Introduction
2. Inputs
3. Calc
4. Trend
Model Structure: Calc
Growth-Adjusted Seasonal Factors Model
11
The first part of the “Calc” brings in the original data, allows for adjustments if
needed, and calculates the normalized monthly amounts.
TrendModel: Calc
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A B C D E F
Calculations Unit: 1
In Use (1 = None; 2 = Initial; 3 = Final) :
Actuals
Adjust-
ments
Adjusted
Actuals
Normalization
Factors
Normalized
Data
Jan-01 27.844 27.844 1.05 26.510
Feb-01 21.631 21.631 0.92 23.459
Mar-01 27.970 27.970 1.07 26.229
Apr-01 25.529 25.529 0.95 26.799
May-01 24.568 24.568 1.06 23.175
Jun-01 24.674 24.674 1.02 24.284
Jul-01 23.878 23.878 0.96 24.883
Aug-01 23.591 23.591 1.10 21.354
Sep-01 25.417 25.417 0.72 35.098
Oct-01 30.229 30.229 1.09 27.692
Nov-01 26.672 26.672 0.99 27.054
Dec-01 25.506 25.506 0.86 29.529
Jan-02 29.943 29.943 1.03 29.056Feb-02 26.255 26.255 0.92 28.474Mar-02 26.743 26.743 0.96 27.806Apr-02 28.761 28.761 1.06 27.239May-02 27.152 27.152 1.06 25.632Jun-02 31.740 31.740 0.97 32.791Jul-02 41.499 41.499 1.02 40.516Aug-02 29.511 29.511 1.05 28.003Sep-02 28.180 28.180 0.97 29.168Oct-02 38.061 38.061 1.10 34.657Nov-02 29.087 29.087 0.93 31.245Dec-02 26.205 26.205 0.89 29.503
Jul-16 22.328 22.328 0.96 23.217
Aug-16 23.490 23.490 1.11 21.141
Sep-16 25.282 25.282 1.01 25.100
Oct-16 22.795 22.795 0.99 22.964
Nov-16 27.327 27.327 0.99 27.708
Dec-16 23.000 23.000 0.92 24.963
Jan-17 0 0 0.99 0
Feb-17 0 0 0.92 0
Mar-17 0 0 1.12 0
A. Actual & Normalized Data
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
12
The next section seasonally-adjusts the data, using one of the 3 sets of
seasonal factors.
TrendModel: Calc
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A B C D E F G H I J K L
Calculations Unit: 1
In Use (1 = None; 2 = Initial; 3 = Final) : 2
Actuals
Adjust-
ments
Adjusted
Actuals
Normalization
Factors
Normalized
Data None Initial Revised In Use
Seasonally-
Adjusted:
Monthly
Seasonally-
Adjusted: 3-
Mo Avg
Jan-01 27.844 27.844 1.05 26.510 1.00 1.00 1.03 1.00 26.406 25.412
Feb-01 21.631 21.631 0.92 23.459 1.00 0.96 0.97 0.96 24.418 25.666
Mar-01 27.970 27.970 1.07 26.229 1.00 1.00 1.01 1.00 26.174 25.849
Apr-01 25.529 25.529 0.95 26.799 1.00 0.99 1.01 0.99 26.954 25.517
May-01 24.568 24.568 1.06 23.175 1.00 0.99 1.00 0.99 23.424 24.712
Jun-01 24.674 24.674 1.02 24.284 1.00 1.02 1.02 1.02 23.756 24.153
Jul-01 23.878 23.878 0.96 24.883 1.00 0.98 0.97 0.98 25.279 24.015
Aug-01 23.591 23.591 1.10 21.354 1.00 0.93 0.89 0.93 23.011 27.767
Sep-01 25.417 25.417 0.72 35.098 1.00 1.00 1.01 1.00 35.011 28.406
Oct-01 30.229 30.229 1.09 27.692 1.00 1.02 1.02 1.02 27.195 29.510
Nov-01 26.672 26.672 0.99 27.054 1.00 1.03 1.00 1.03 26.326 27.069
Dec-01 25.506 25.506 0.86 29.529 1.00 1.07 1.07 1.07 27.685 27.651
Jan-02 29.943 29.943 1.03 29.056 1.00 1.00 1.03 1.00 28.941 28.754Feb-02 26.255 26.255 0.92 28.474 1.00 0.96 0.97 0.96 29.637 28.775Mar-02 26.743 26.743 0.96 27.806 1.00 1.00 1.01 1.00 27.747 28.260Apr-02 28.761 28.761 1.06 27.239 1.00 0.99 1.01 0.99 27.397 27.017May-02 27.152 27.152 1.06 25.632 1.00 0.99 1.00 0.99 25.908 28.461Jun-02 31.740 31.740 0.97 32.791 1.00 1.02 1.02 1.02 32.079 33.049Jul-02 41.499 41.499 1.02 40.516 1.00 0.98 0.97 0.98 41.160 34.472Aug-02 29.511 29.511 1.05 28.003 1.00 0.93 0.89 0.93 30.177 33.477Sep-02 28.180 28.180 0.97 29.168 1.00 1.00 1.01 1.00 29.095 31.102Oct-02 38.061 38.061 1.10 34.657 1.00 1.02 1.02 1.02 34.034 31.178Nov-02 29.087 29.087 0.93 31.245 1.00 1.03 1.00 1.03 30.404 30.700Dec-02 26.205 26.205 0.89 29.503 1.00 1.07 1.07 1.07 27.660 29.293
Jul-16 22.328 22.328 0.96 23.217 1.00 0.98 0.97 0.98 23.585 24.695
Aug-16 23.490 23.490 1.11 21.141 1.00 0.93 0.89 0.93 22.782 23.801
Sep-16 25.282 25.282 1.01 25.100 1.00 1.00 1.01 1.00 25.037 23.457
Oct-16 22.795 22.795 0.99 22.964 1.00 1.02 1.02 1.02 22.552 24.850
Nov-16 27.327 27.327 0.99 27.708 1.00 1.03 1.00 1.03 26.963 24.306
Dec-16 23.000 23.000 0.92 24.963 1.00 1.07 1.07 1.07 23.404 25.183
Jan-17 0 0 0.99 0 1.00 1.00 1.03 1.00
Feb-17 0 0 0.92 0 1.00 0.96 0.97 0.96
Mar-17 0 0 1.12 0 1.00 1.00 1.01 1.00
Seasonal Factors
A. Actual & Normalized Data B. Seasonally-Adjusted Data
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
13
The 3rd section estimates the data trend, using the Growth Rates and Events
that will be estimated in the “Trend” tab.
TrendModel: Calc
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A E F G H I J K L M N O P
Calculations1
In Use (1 = None; 2 = Initial; 3 = Final) : 2 Start: 25.000
Normalization
Factors
Normalized
Data None Initial "Final" In Use
Seasonally-
Adjusted:
Monthly
Seasonally-
Adjusted: 3-
Mo Avg
Growth
Rate
1-Time
Events
Estimated
Trend
Estimated
Trend
Values
Jan-01 1.05 26.510 1.00 1.00 1.03 1.00 26.406 25.412 2.0% 0.0% 25.042 26.406
Feb-01 0.92 23.459 1.00 0.96 0.97 0.96 24.418 25.666 2.0% 0.0% 25.083 22.221
Mar-01 1.07 26.229 1.00 1.00 1.01 1.00 26.174 25.849 2.0% 0.0% 25.125 26.849
Apr-01 0.95 26.799 1.00 0.99 1.01 0.99 26.954 25.517 2.0% 0.0% 25.167 23.836
May-01 1.06 23.175 1.00 0.99 1.00 0.99 23.424 24.712 2.0% 0.0% 25.209 26.441
Jun-01 1.02 24.284 1.00 1.02 1.02 1.02 23.756 24.153 2.0% 0.0% 25.251 26.226
Jul-01 0.96 24.883 1.00 0.98 0.97 0.98 25.279 24.015 2.0% 0.0% 25.293 23.892
Aug-01 1.10 21.354 1.00 0.93 0.89 0.93 23.011 27.767 2.0% 0.0% 25.335 25.973
Sep-01 0.72 35.098 1.00 1.00 1.01 1.00 35.011 28.406 2.0% 30.0% 32.991 23.950
Oct-01 1.09 27.692 1.00 1.02 1.02 1.02 27.195 29.510 2.0% -20.0% 26.437 29.386
Nov-01 0.99 27.054 1.00 1.03 1.00 1.03 26.326 27.069 2.0% 0.0% 26.481 26.829
Dec-01 0.86 29.529 1.00 1.07 1.07 1.07 27.685 27.651 2.0% 0.0% 26.525 24.437
Jan-02 1.03 29.056 1.00 1.00 1.03 1.00 28.941 28.754 2.0% 0.0% 26.569 27.489Feb-02 0.92 28.474 1.00 0.96 0.97 0.96 29.637 28.775 2.0% 0.0% 26.613 23.576Mar-02 0.96 27.806 1.00 1.00 1.01 1.00 27.747 28.260 2.0% 0.0% 26.658 25.693Apr-02 1.06 27.239 1.00 0.99 1.01 0.99 27.397 27.017 2.0% 0.0% 26.702 28.032May-02 1.06 25.632 1.00 0.99 1.00 0.99 25.908 28.461 2.0% 0.0% 26.747 28.031Jun-02 0.97 32.791 1.00 1.02 1.02 1.02 32.079 33.049 2.0% 0.0% 26.791 26.508Jul-02 1.02 40.516 1.00 0.98 0.97 0.98 41.160 34.472 1.0% 0.0% 26.813 27.034Aug-02 1.05 28.003 1.00 0.93 0.89 0.93 30.177 33.477 1.0% 0.0% 26.836 26.244Sep-02 0.97 29.168 1.00 1.00 1.01 1.00 29.095 31.102 1.0% 0.0% 26.858 26.014Oct-02 1.10 34.657 1.00 1.02 1.02 1.02 34.034 31.178 1.0% 0.0% 26.881 30.061Nov-02 0.93 31.245 1.00 1.03 1.00 1.03 30.404 30.700 1.0% 0.0% 26.903 25.738Dec-02 0.89 29.503 1.00 1.07 1.07 1.07 27.660 29.293 1.0% 0.0% 26.925 25.509
Jul-16 0.96 23.217 1.00 0.98 0.97 0.98 23.585 24.695 1.0% 0.0% 30.841 29.197
Aug-16 1.11 21.141 1.00 0.93 0.89 0.93 22.782 23.801 1.0% 0.0% 30.867 31.826
Sep-16 1.01 25.100 1.00 1.00 1.01 1.00 25.037 23.457 1.0% 0.0% 30.892 31.195
Oct-16 0.99 22.964 1.00 1.02 1.02 1.02 22.552 24.850 0.0% 0.0% 30.892 31.226
Nov-16 0.99 27.708 1.00 1.03 1.00 1.03 26.963 24.306 0.0% 0.0% 30.892 31.310
Dec-16 0.92 24.963 1.00 1.07 1.07 1.07 23.404 25.183 0.0% 0.0% 30.892 30.359
Jan-17 0.99 0 1.00 1.00 1.03 1.00 0.0% 0.0%
Feb-17 0.92 0 1.00 0.96 0.97 0.96 0.0% 2.0%
Mar-17 1.12 0 1.00 1.00 1.01 1.00 0.0% 0.0%
Seasonal Factors
A. Actual & Normalized Data B. Seasonally-Adjusted Data C. Estimated Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
14
The 4th section is the forecast, which takes the estimated trend and
extrapolates it using the assumptions for future growth rate & events.
TrendModel: Calc
1
2
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
197
198
199
200
201
202
203
204
205
A M N O P Q R
Calculations
Start: 25.000
Growth
Rate
1-Time
Events
Estimated
Trend
Estimated
Trend
Values
Extrapolated
Trend
Extrapolated
Trend Values
(= Forecast)
Jan-01 2.0% 0.0% 25.042 26.406
Feb-01 2.0% 0.0% 25.083 22.221
Mar-01 2.0% 0.0% 25.125 26.849
Apr-01 2.0% 0.0% 25.167 23.836
May-01 2.0% 0.0% 25.209 26.441
Jun-01 2.0% 0.0% 25.251 26.226
Jul-01 2.0% 0.0% 25.293 23.892
Aug-01 2.0% 0.0% 25.335 25.973
Sep-01 2.0% 30.0% 32.991 23.950
Oct-01 2.0% -20.0% 26.437 29.386
Nov-01 2.0% 0.0% 26.481 26.829
Dec-01 2.0% 0.0% 26.525 24.437
Jan-02 2.0% 0.0% 26.569 27.489Feb-02 2.0% 0.0% 26.613 23.576Mar-02 2.0% 0.0% 26.658 25.693Apr-02 2.0% 0.0% 26.702 28.032May-02 2.0% 0.0% 26.747 28.031Jun-02 2.0% 0.0% 26.791 26.508Jul-02 1.0% 0.0% 26.813 27.034Aug-02 1.0% 0.0% 26.836 26.244Sep-02 1.0% 0.0% 26.858 26.014Oct-02 1.0% 0.0% 26.881 30.061Nov-02 1.0% 0.0% 26.903 25.738Dec-02 1.0% 0.0% 26.925 25.509
Jul-16 1.0% 0.0% 30.841 29.197
Aug-16 1.0% 0.0% 30.867 31.826
Sep-16 1.0% 0.0% 30.892 31.195
Oct-16 0.0% 0.0% 30.892 31.226
Nov-16 0.0% 0.0% 30.892 31.310
Dec-16 0.0% 0.0% 30.892 30.359
Jan-17 0.0% 0.0% 30.892 30.614
Feb-17 0.0% 2.0% 31.510 27.874
Mar-17 0.0% 0.0% 31.510 35.249
C. Estimated Trend D. Forecasts
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
15
The 5th & final section picks up the past & projected trend, as well as the past
actuals and extrapolated trend values.
TrendModel: Calc
1
2
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
197
198
199
200
201
202
203
204
205
A B O P Q R S T U
Calculations
25.000
Actuals
Estimated
Trend
Estimated
Trend
Values
Extrapolated
Trend
Extrapolated
Trend Values
(= Forecast)
Estimated (&
Extrapolated)
Trend
Actual (&
Extrapolated)
Values
Estimate vs
Actual: Diff
Jan-01 27.844 25.042 26.406 25.042 27.844 (2.802)
Feb-01 21.631 25.083 22.221 25.083 21.631 3.452
Mar-01 27.970 25.125 26.849 25.125 27.970 (2.845)
Apr-01 25.529 25.167 23.836 25.167 25.529 (0.362)
May-01 24.568 25.209 26.441 25.209 24.568 0.641
Jun-01 24.674 25.251 26.226 25.251 24.674 0.577
Jul-01 23.878 25.293 23.892 25.293 23.878 1.415
Aug-01 23.591 25.335 25.973 25.335 23.591 1.745
Sep-01 25.417 32.991 23.950 32.991 25.417 7.574
Oct-01 30.229 26.437 29.386 26.437 30.229 (3.792)
Nov-01 26.672 26.481 26.829 26.481 26.672 (0.191)
Dec-01 25.506 26.525 24.437 26.525 25.506 1.019
Jan-02 29.943 26.569 27.489 26.569 29.943 (3.374)Feb-02 26.255 26.613 23.576 26.613 26.255 0.358Mar-02 26.743 26.658 25.693 26.658 26.743 (0.085)Apr-02 28.761 26.702 28.032 26.702 28.761 (2.059)May-02 27.152 26.747 28.031 26.747 27.152 (0.405)Jun-02 31.740 26.791 26.508 26.791 31.740 (4.948)Jul-02 41.499 26.813 27.034 26.813 41.499 (14.685)Aug-02 29.511 26.836 26.244 26.836 29.511 (2.675)Sep-02 28.180 26.858 26.014 26.858 28.180 (1.322)Oct-02 38.061 26.881 30.061 26.881 38.061 (11.180)Nov-02 29.087 26.903 25.738 26.903 29.087 (2.184)Dec-02 26.205 26.925 25.509 26.925 26.205 0.720
Jul-16 22.328 30.841 29.197 30.841 22.328 6.869
Aug-16 23.490 30.867 31.826 30.867 23.490 8.336
Sep-16 25.282 30.892 31.195 30.892 25.282 5.913
Oct-16 22.795 30.892 31.226 30.892 22.795 8.431
Nov-16 27.327 30.892 31.310 30.892 27.327 3.983
Dec-16 23.000 30.892 30.359 30.892 23.000 7.359
Jan-17 0 30.892 30.614 30.892 30.614 0
Feb-17 0 31.510 27.874 31.510 27.874 0
Mar-17 0 31.510 35.249 31.510 35.249 0
E. Estimate & ActualA. Actual & Normalized DataC. Estimated Trend D. Forecasts
1. Introduction
2. Inputs
3. Calc
4. Trend
Revise Col. U & its explanation.
Change next page and start page
showing this as well
Growth-Adjusted Seasonal Factors Model
16
The bottom of the “Calc” tab calculates annual totals for all the columns.
TrendModel: Calc
1
2
7
8
9
10
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
A B C D E F G H I J K L M N O P Q R S T U
Calculations Unit: 1
In Use (1 = None; 2 = Initial; 3 = Final) : 2 Start: 25.000
Actuals
Adjust-
ments
Adjusted
Actuals
Normalization
Factors
Normalized
Data None Initial "Final" In Use
Seasonally-
Adjusted:
Monthly
Seasonally-
Adjusted: 3-
Mo Avg
Growth
Rate
1-Time
Events
Estimated
Trend
Estimated
Trend
Values
Extrapolated
Trend
Extrapolated
Trend Values
(= Forecast)
Estimated (&
Extrapolated)
Trend
Actual (&
Extrapolated)
Values
Estimate vs
Actual: Diff
Annual Totals
2001 308 0 308 0.983 316 1.000 1.000 1.000 1.000 316 316 2.0% 10.0% 314 306 0 0 314 308 6
2002 363 0 363 0.997 364 1.000 1.000 1.000 1.000 364 365 1.5% 0.0% 321 320 0 0 321 363 (42)
2003 352 0 352 1.000 352 1.000 1.000 1.000 1.000 352 353 1.0% 0.0% 325 325 0 0 325 352 (28)
2004 370 0 370 1.003 370 1.000 1.000 1.000 1.000 369 367 1.0% 0.0% 328 329 0 0 328 370 (42)
2005 415 0 415 1.004 414 1.000 1.000 1.000 1.000 414 416 1.0% 0.0% 331 332 0 0 331 415 (84)
2006 458 0 458 0.997 460 1.000 1.000 1.000 1.000 460 459 1.0% 0.0% 335 334 0 0 335 458 (124)
2007 532 0 532 0.999 531 1.000 1.000 1.000 1.000 533 537 1.0% 0.0% 338 338 0 0 338 532 (194)
2008 660 0 660 1.003 656 1.000 1.000 1.000 1.000 656 650 1.0% 0.0% 342 343 0 0 342 660 (319)
2009 549 0 549 0.999 550 1.000 1.000 1.000 1.000 551 551 1.0% 0.0% 345 344 0 0 345 549 (204)
2010 445 0 445 0.999 445 1.000 1.000 1.000 1.000 446 447 1.0% 0.0% 348 348 0 0 348 445 (96)
2011 384 0 384 1.003 381 1.000 1.000 1.000 1.000 382 381 1.0% 0.0% 352 353 0 0 352 384 (32)
2012 287 0 287 0.998 288 1.000 1.000 1.000 1.000 288 288 1.0% 0.0% 355 354 0 0 355 287 69
2013 261 0 261 0.996 262 1.000 1.000 1.000 1.000 262 262 1.0% 0.0% 359 357 0 0 359 261 98
2014 262 0 262 1.000 262 1.000 1.000 1.000 1.000 262 261 1.0% 0.0% 363 362 0 0 363 262 101
2015 299 0 299 0.999 300 1.000 1.000 1.000 1.000 300 301 1.0% 0.0% 366 366 0 0 366 299 67
2016 315 0 315 1.002 315 1.000 1.000 1.000 1.000 315 315 0.8% 0.0% 370 370 0 0 370 315 55
2017 0 0 0 0.997 0 1.000 1.000 1.000 1.000 0 0 0.0% 2.0% 0 0 378 376 378 376 0
2018 0 0 0 0.999 0 1.000 1.000 1.000 1.000 0 0 0.0% 0.0% 0 0 378 377 378 377 0
2019 0 0 0 0.996 0 1.000 1.000 1.000 1.000 0 0 0.0% 0.0% 0 0 378 376 378 376 0
2020 0 0 0 1.004 0 1.000 1.000 1.000 1.000 0 0 0.0% 0.0% 0 0 378 379 378 379 0
E. Estimate & Actual
Seasonal Factors
A. Actual & Normalized Data B. Seasonally-Adjusted Data C. Estimated Trend D. Forecasts
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
17
The “Trend” tab is divided into
three sections.
TrendModel: Trend
1
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
29
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31
32
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35
36
37
38
39
40
41
42
43
49
50
51
52
53
54
55
56
57
58
59
60
61
62
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
139
140
141
142
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152
153
154
155
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
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206
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227
228
229
230
231
232
233
234
235
236
A C D E F G H I J K L M N O P Q R S X Y Z AA AB AC AD AE AF AG AH AI AJ
Estimating Trend Seasonal Factors In Use: Initial 2
(1 = None; 2 = Initial; 3 = Final)
Growth Rate
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Feb 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Mar 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Apr 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
May 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Jun 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Jul 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Aug 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Sep 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Oct 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0%
Nov 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0%
Dec 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0%
Start
25.0
Events
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan
Feb 2.0%
Mar
Apr
May
Jun
Jul
Aug
Sep 30.0%
Oct -20.0%
Nov
Dec
Actuals vs Estimate by Year
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Actual 307.5 363.1 352.4 369.6 415.1 458.5 532.0 660.3 549.3 444.7 383.9 286.8 260.7 261.9 299.1 315.5 0.0
Est 306.4 319.9 324.8 329.0 332.4 333.5 337.5 342.5 344.5 348.1 352.7 354.4 357.3 362.4 365.8 370.4 376.1
Diff -1.1 -43.2 -27.6 -40.6 -82.7 -125.0 -194.5 -317.8 -204.8 -96.6 -31.2 67.6 96.7 100.5 66.7 54.9
% Diff -0.3% -11.9% -7.8% -11.0% -19.9% -27.3% -36.6% -48.1% -37.3% -21.7% -8.1% 23.6% 37.1% 38.4% 22.3% 17.4%
Total
2001-16 YTD
Actual 6,260 315.5
Est 5,482 370.4
Diff (779) 54.9
% Diff -12.4% 17.4%
Seasonal Factors
Normalized Data
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 26.5 29.1 29.9 34.2 33.2 39.6 38.3 58.1 46.4 35.6 33.2 24.7 22.0 20.7 24.5 31.2 0.0
Feb 23.5 28.5 27.5 30.6 33.0 37.5 40.0 47.0 54.6 35.5 31.8 24.4 22.2 22.1 23.2 30.9 0.0
Mar 26.2 27.8 29.9 30.7 35.6 35.9 43.9 55.7 61.8 33.2 31.9 24.8 22.4 22.1 24.1 28.4 0.0
Apr 26.8 27.2 29.6 31.9 35.8 37.2 40.2 43.9 53.5 41.0 27.8 24.6 22.2 21.8 22.6 25.7 0.0
May 23.2 25.6 31.0 31.5 32.2 41.5 41.3 42.5 52.6 54.4 28.5 26.4 21.9 19.4 21.8 25.6 0.0
Jun 24.3 32.8 31.5 27.1 32.1 41.4 45.0 50.5 43.7 43.5 30.0 26.4 26.0 21.1 24.6 28.3 0.0
Jul 24.9 40.5 30.2 29.3 31.5 38.7 49.0 60.5 38.4 36.5 27.3 24.5 20.5 19.2 23.0 23.2 0.0
Aug 21.4 28.0 25.1 25.9 30.6 33.3 55.4 44.6 41.2 32.0 43.6 20.2 19.1 17.8 27.5 21.1 0.0
Sep 35.1 29.2 29.7 27.7 36.1 37.3 40.3 70.1 42.8 32.2 35.0 23.9 21.8 21.4 27.8 25.1 0.0
Oct 27.7 34.7 30.0 32.9 40.7 39.1 41.6 75.7 41.4 33.9 34.5 20.2 20.8 26.7 26.4 23.0 0.0
Nov 27.1 31.2 27.8 32.4 36.4 40.4 52.2 57.3 35.2 33.9 29.6 23.1 20.3 22.4 25.2 27.7 0.0
Dec 29.5 29.5 29.6 35.2 36.8 38.2 44.1 50.2 38.1 33.7 27.6 24.7 23.0 27.6 28.9 25.0 0.0
Growth Rate (Monthly Basis)
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Feb 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 2.0%
Mar 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Apr 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
May 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Jun 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Jul 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Aug 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Sep 30.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Oct -19.9% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0%
Nov 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0%
Dec 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0%
Cumulative Growth Rate
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Feb 0.3% 0.3% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 2.0%
Mar 0.5% 0.5% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 2.0%
Apr 0.7% 0.7% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 2.0%
May 0.8% 0.8% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 2.0%
Jun 1.0% 1.0% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 2.0%
Jul 1.2% 1.1% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 2.0%
Aug 1.3% 1.2% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 2.0%
Sep 32.0% 1.3% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 2.0%
Oct 5.7% 1.3% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 2.0%
Nov 5.9% 1.4% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.8% 2.0%
Dec 6.1% 1.5% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.8% 2.0%
Avg 4.6% 0.9% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 1.8%
Indexed Cumulative Growth
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 0.96 0.99 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.98
Feb 0.96 0.99 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Mar 0.96 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Apr 0.96 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
May 0.96 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Jun 0.97 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Jul 0.97 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Aug 0.97 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Sep 1.26 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Oct 1.01 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Nov 1.01 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Dec 1.01 1.01 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Avg 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
Growth-Adjusted Normalized Data
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 27.7 29.3 30.1 34.3 33.3 39.8 38.5 58.3 46.7 35.8 33.3 24.8 22.1 20.8 24.6 31.3 0.0
Feb 24.5 28.6 27.6 30.7 33.1 37.6 40.1 47.2 54.8 35.6 31.9 24.5 22.3 22.2 23.3 31.0 0.0
Mar 27.3 27.9 30.0 30.8 35.7 36.0 44.0 55.9 61.9 33.3 32.0 24.9 22.4 22.1 24.2 28.4 0.0
Apr 27.9 27.3 29.7 32.0 35.9 37.2 40.3 44.0 53.6 41.1 27.9 24.6 22.2 21.8 22.6 25.8 0.0
May 24.1 25.7 31.0 31.5 32.2 41.5 41.4 42.6 52.6 54.5 28.6 26.4 21.9 19.4 21.9 25.6 0.0
Jun 25.2 32.8 31.5 27.2 32.1 41.5 45.1 50.6 43.7 43.6 30.0 26.4 26.0 21.1 24.6 28.3 0.0
Jul 25.7 40.5 30.2 29.3 31.5 38.6 49.0 60.4 38.4 36.5 27.2 24.5 20.5 19.2 23.0 23.2 0.0
Aug 22.1 27.9 25.1 25.9 30.6 33.2 55.4 44.6 41.1 32.0 43.6 20.2 19.0 17.8 27.4 21.1 0.0
Sep 27.8 29.1 29.7 27.6 36.0 37.2 40.2 70.0 42.7 32.1 34.9 23.9 21.7 21.3 27.8 25.0 0.0
Oct 27.4 34.5 29.9 32.8 40.6 39.0 41.5 75.5 41.2 33.8 34.4 20.2 20.7 26.6 26.4 22.9 0.0
Nov 26.7 31.1 27.7 32.3 36.3 40.3 52.0 57.1 35.0 33.7 29.5 23.0 20.3 22.3 25.1 27.6 0.0
Dec 29.1 29.3 29.5 35.0 36.7 38.0 43.9 50.0 37.9 33.6 27.5 24.6 22.9 27.5 28.7 24.9 0.0
Avg 26.3 30.3 29.3 30.8 34.5 38.3 44.3 54.7 45.8 37.1 31.7 24.0 21.8 21.8 25.0 26.3 0.0
0.2% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
Growth-Adjusted Normalized Data: Factored Max Permitted Standard Deviations: 2.0
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Avg Std Dev Low High Wtd Avg
Jan 1.05 0.97 1.03 1.11 0.97 1.04 0.87 1.07 1.02 0.96 1.05 1.03 1.01 0.95 0.98 1.19 1.02 0.07 0.87 1.17 1.03
Feb 0.93 0.94 0.94 1.00 0.96 0.98 0.91 0.86 1.20 0.96 1.01 1.02 1.02 1.02 0.93 1.18 0.99 0.09 0.81 1.17 0.97
Mar 1.04 0.92 1.02 1.00 1.03 0.94 0.99 1.02 1.35 0.90 1.01 1.04 1.03 1.01 0.97 1.08 1.02 0.10 0.82 1.22 1.01
Apr 1.06 0.90 1.01 1.04 1.04 0.97 0.91 0.81 1.17 1.11 0.88 1.03 1.02 1.00 0.91 0.98 0.99 0.09 0.80 1.17 1.01
May 0.91 0.85 1.06 1.02 0.93 1.08 0.93 0.78 1.15 1.47 0.90 1.10 1.00 0.89 0.88 0.98 1.00 0.16 0.67 1.32 1.00
Jun 0.96 1.08 1.07 0.88 0.93 1.08 1.02 0.92 0.95 1.17 0.95 1.10 1.19 0.97 0.99 1.08 1.02 0.09 0.84 1.20 1.02
Jul 0.98 1.33 1.03 0.95 0.91 1.01 1.11 1.11 0.84 0.98 0.86 1.02 0.94 0.88 0.92 0.88 0.98 0.12 0.74 1.23 0.97
Aug 0.84 0.92 0.86 0.84 0.89 0.87 1.25 0.82 0.90 0.86 1.37 0.84 0.87 0.81 1.10 0.80 0.93 0.17 0.59 1.26 0.89
Sep 1.06 0.96 1.01 0.90 1.04 0.97 0.91 1.28 0.93 0.87 1.10 0.99 0.99 0.98 1.11 0.95 1.00 0.10 0.80 1.21 1.01
Oct 1.04 1.14 1.02 1.07 1.18 1.02 0.94 1.38 0.90 0.91 1.08 0.84 0.95 1.22 1.06 0.87 1.04 0.14 0.75 1.32 1.02
Nov 1.02 1.03 0.95 1.05 1.05 1.05 1.17 1.04 0.76 0.91 0.93 0.96 0.93 1.02 1.01 1.05 1.00 0.09 0.81 1.18 1.00
Dec 1.11 0.97 1.00 1.14 1.06 0.99 0.99 0.91 0.83 0.90 0.87 1.02 1.05 1.26 1.15 0.95 1.01 0.11 0.79 1.24 1.07
Avg 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.11 0.78 1.22 1.00
Data Accepted?
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Total
Jan 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0
Feb 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0
Mar 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1
Apr 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
May 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1
Jun 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Jul 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Aug 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1
Sep 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1
Oct 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1
Nov 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1
Dec 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1
OK? 1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 8
Use Std
Dev? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Seasonal
Factor
Weights
1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 0 8
Accepted Range
022.0
24.0
26.0
28.0
30.0
32.0
34.0
36.0
38.0
40.0
Jan-01 Jan-02 Jan-03 Jan-04
Sales
Volumes
(Billions)
NYSE Monthly Sales Volumes
Seasonally-Adjusted
Actual (& Extrapolated) Values
Seasonally-Adjusted: Monthly
Seasonally-Adjusted: 3-Mo Avg
0.70
0.80
0.90
1.00
1.10
1.20
1.30
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Seasonal Factors Final
Initial
Low
High
Trend
Estimates
Seasonal
Factors
Calculation
Chart
1. Introduction
2. Inputs
3. Calc
4. Trend
Model Structure: Trend
Growth-Adjusted Seasonal Factors Model
1
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
49
50
51
52
53
54
55
56
57
58
59
60
61
62
A C D E F G H I J K L M N O P Q R S X
Estimating Trend
Growth Rate
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Feb 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Mar 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Apr 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
May 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Jun 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Jul 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Aug 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Sep 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Oct 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0%
Nov 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0%
Dec 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0%
Start
25.0
Events
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan
Feb 2.0%
Mar
Apr
May
Jun
Jul 10.0%
Aug
Sep 30.0%
Oct -20.0%
Nov
Dec
Actuals vs Estimate by Year
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Actual 307.5 363.1 352.4 369.6 415.1 458.5 532.0 660.3 549.3 444.7 383.9 286.8 260.7 261.9 299.1 315.5 0.0
Est 306.4 336.0 357.3 361.9 365.6 366.9 371.3 376.8 378.9 382.9 387.9 389.9 393.1 398.7 402.4 407.4 413.8
Diff -1.1 -27.1 4.9 -7.7 -49.4 -91.6 -160.8 -283.5 -170.4 -61.8 4.1 103.1 132.4 136.8 103.3 91.9
% Diff -0.3% -7.5% 1.4% -2.1% -11.9% -20.0% -30.2% -42.9% -31.0% -13.9% 1.1% 35.9% 50.8% 52.2% 34.5% 29.1%
Total
2001-16 YTD
Actual 6,260 315.5
Est 5,983 407.4
Diff (277) 91.9
% Diff -4.4% 29.1%
22.0
24.0
26.0
28.0
30.0
32.0
34.0
36.0
38.0
40.0
18
The “Estimating Trend” section is the steering wheel for the model; it’s where
you insert your monthly estimates of the growth rate and events.
TrendModel: Trend
Growth
Rates
Events
Starting
Point
Actuals
vs
Estimate
Model Structure: Trend Estimates
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
1
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
49
50
51
52
53
54
55
56
57
58
59
60
61
62
A C D E F
Estimating Trend
Growth Rate
2001 2002 2003 2004
Jan 2.0% 2.0% 1.0% 1.0%
Feb 2.0% 2.0% 1.0% 1.0%
Mar 2.0% 2.0% 1.0% 1.0%
Apr 2.0% 2.0% 1.0% 1.0%
May 2.0% 2.0% 1.0% 1.0%
Jun 2.0% 2.0% 1.0% 1.0%
Jul 2.0% 1.0% 1.0% 1.0%
Aug 2.0% 1.0% 1.0% 1.0%
Sep 2.0% 1.0% 1.0% 1.0%
Oct 2.0% 1.0% 1.0% 1.0%
Nov 2.0% 1.0% 1.0% 1.0%
Dec 2.0% 1.0% 1.0% 1.0%
Start
25.0
Events
2001 2002 2003 2004
Jan
Feb
Mar
Apr
May
Jun
Jul 10.0%
Aug
Sep 30.0%
Oct -20.0%
Nov
Dec
Actuals vs Estimate by Year
2001 2002 2003 2004
Actual 307.5 363.1 352.4 369.6
Est 306.4 336.0 357.3 361.9
Diff -1.1 -27.1 4.9 -7.7
% Diff -0.3% -7.5% 1.4% -2.1%
19
The Growth Rates are the estimates of the annual rate at which the data is
growing; conditional formatting highlights changes in the rate.
TrendModel: Trend
Growth
Rates
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
1
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
49
50
51
52
53
54
55
56
57
58
59
60
61
62
A C D E F
Estimating Trend
Growth Rate
2001 2002 2003 2004
Jan 2.0% 2.0% 1.0% 1.0%
Feb 2.0% 2.0% 1.0% 1.0%
Mar 2.0% 2.0% 1.0% 1.0%
Apr 2.0% 2.0% 1.0% 1.0%
May 2.0% 2.0% 1.0% 1.0%
Jun 2.0% 2.0% 1.0% 1.0%
Jul 2.0% 1.0% 1.0% 1.0%
Aug 2.0% 1.0% 1.0% 1.0%
Sep 2.0% 1.0% 1.0% 1.0%
Oct 2.0% 1.0% 1.0% 1.0%
Nov 2.0% 1.0% 1.0% 1.0%
Dec 2.0% 1.0% 1.0% 1.0%
Start
25.0
Events
2001 2002 2003 2004
Jan
Feb
Mar
Apr
May
Jun
Jul 10.0%
Aug
Sep 30.0%
Oct -20.0%
Nov
Dec
Actuals vs Estimate by Year
2001 2002 2003 2004
Actual 307.5 363.1 352.4 369.6
Est 306.4 336.0 357.3 361.9
Diff -1.1 -27.1 4.9 -7.7
% Diff -0.3% -7.5% 1.4% -2.1%
20
The Starting Point is the approximate level at the outset of the period being
modeled.
TrendModel: Trend
Starting
Point
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
1
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
49
50
51
52
53
54
55
56
57
58
59
60
61
62
A C D E F
Estimating Trend
Growth Rate
2001 2002 2003 2004
Jan 2.0% 2.0% 1.0% 1.0%
Feb 2.0% 2.0% 1.0% 1.0%
Mar 2.0% 2.0% 1.0% 1.0%
Apr 2.0% 2.0% 1.0% 1.0%
May 2.0% 2.0% 1.0% 1.0%
Jun 2.0% 2.0% 1.0% 1.0%
Jul 2.0% 1.0% 1.0% 1.0%
Aug 2.0% 1.0% 1.0% 1.0%
Sep 2.0% 1.0% 1.0% 1.0%
Oct 2.0% 1.0% 1.0% 1.0%
Nov 2.0% 1.0% 1.0% 1.0%
Dec 2.0% 1.0% 1.0% 1.0%
Start
25.0
Events
2001 2002 2003 2004
Jan
Feb
Mar
Apr
May
Jun
Jul 10.0%
Aug
Sep 30.0%
Oct -20.0%
Nov
Dec
Actuals vs Estimate by Year
2001 2002 2003 2004
Actual 307.5 363.1 352.4 369.6
Est 306.4 336.0 357.3 361.9
Diff -1.1 -27.1 4.9 -7.7
% Diff -0.3% -7.5% 1.4% -2.1%
21
Events are the estimates of when a step function takes place, when there is a
sudden shift in the level of the data. Most months do not have events.
TrendModel: Trend
Events
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
1
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
49
50
51
52
53
54
55
56
57
58
59
60
61
62
A C D E F
Estimating Trend
Growth Rate
2001 2002 2003 2004
Jan 2.0% 2.0% 1.0% 1.0%
Feb 2.0% 2.0% 1.0% 1.0%
Mar 2.0% 2.0% 1.0% 1.0%
Apr 2.0% 2.0% 1.0% 1.0%
May 2.0% 2.0% 1.0% 1.0%
Jun 2.0% 2.0% 1.0% 1.0%
Jul 2.0% 1.0% 1.0% 1.0%
Aug 2.0% 1.0% 1.0% 1.0%
Sep 2.0% 1.0% 1.0% 1.0%
Oct 2.0% 1.0% 1.0% 1.0%
Nov 2.0% 1.0% 1.0% 1.0%
Dec 2.0% 1.0% 1.0% 1.0%
Start
25.0
Events
2001 2002 2003 2004
Jan
Feb
Mar
Apr
May
Jun
Jul 10.0%
Aug
Sep 30.0%
Oct -20.0%
Nov
Dec
Actuals vs Estimate by Year
2001 2002 2003 2004
Actual 307.5 363.1 352.4 369.6
Est 306.4 336.0 357.3 361.9
Diff -1.1 -27.1 4.9 -7.7
% Diff -0.3% -7.5% 1.4% -2.1%
22
The Actual vs Estimate section compares each year’s totals and calculates the
difference between the estimated trend and actuals.
TrendModel: Trend
Actuals
vs
Estimate
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
1
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
49
50
51
52
53
54
55
56
57
58
59
60
61
62
A C D E F G H I J K L M N O P Q R S X
Estimating Trend
Growth Rate
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Feb 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Mar 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Apr 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
May 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Jun 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Jul 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Aug 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Sep 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Oct 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0%
Nov 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0%
Dec 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0%
Start
25.0
Events
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan
Feb 2.0%
Mar
Apr
May
Jun
Jul 10.0%
Aug
Sep 30.0%
Oct -20.0%
Nov
Dec
Actuals vs Estimate by Year
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Actual 307.5 363.1 352.4 369.6 415.1 458.5 532.0 660.3 549.3 444.7 383.9 286.8 260.7 261.9 299.1 315.5 0.0
Est 306.4 336.0 357.3 361.9 365.6 366.9 371.3 376.8 378.9 382.9 387.9 389.9 393.1 398.7 402.4 407.4 413.8
Diff -1.1 -27.1 4.9 -7.7 -49.4 -91.6 -160.8 -283.5 -170.4 -61.8 4.1 103.1 132.4 136.8 103.3 91.9
% Diff -0.3% -7.5% 1.4% -2.1% -11.9% -20.0% -30.2% -42.9% -31.0% -13.9% 1.1% 35.9% 50.8% 52.2% 34.5% 29.1%
Total
2001-16 YTD
Actual 6,260 315.5
Est 5,983 407.4
Diff (277) 91.9
% Diff -4.4% 29.1%
22.0
24.0
26.0
28.0
30.0
32.0
34.0
36.0
38.0
40.0
23
The Total Actual vs Estimate table shows how actuals and estimates compare
over the entire modeled time period; it also compares current year-to-date.
TrendModel: Trend
Actuals
vs
Estimate
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
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A C D E F G H I J K L M N O P Q R S
Estimating Trend
Growth Rate
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Feb 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Mar 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Apr 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
May 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Jun 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Jul 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Aug 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Sep 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Oct 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0%
Nov 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0%
Dec 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0%
Start
25.0
Events
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan
Feb 2.0%
Mar
Apr
May
Jun
Jul 10.0%
Aug
Sep 30.0%
Oct -20.0%
Nov
Dec
Actuals vs Estimate by Year
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Actual 307.5 363.1 352.4 369.6 415.1 458.5 532.0 660.3 549.3 444.7 383.9 286.8 260.7 261.9 299.1 315.5 0.0
Est 306.4 336.0 357.3 361.9 365.6 366.9 371.3 376.8 378.9 382.9 387.9 389.9 393.1 398.7 402.4 407.4 413.8
Diff -1.1 -27.1 4.9 -7.7 -49.4 -91.6 -160.8 -283.5 -170.4 -61.8 4.1 103.1 132.4 136.8 103.3 91.9
% Diff -0.3% -7.5% 1.4% -2.1% -11.9% -20.0% -30.2% -42.9% -31.0% -13.9% 1.1% 35.9% 50.8% 52.2% 34.5% 29.1%
Total
2001-16 YTD
Actual 6,260 315.5
Est 5,983 407.4
Diff (277) 91.9
% Diff -4.4% 29.1%
Other Info (e.g. Price Changes)
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
24
While hidden here because it isn’t applicable, there is a section here for
“Other Info” that may provide a useful reference.
TrendModel: Trend
Other
Info
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
25
The Seasonal Factors
Calculation section takes the
Normalized data, and adjusts
for growth & events.
TrendModel: Trend
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A C D E F G H I J K L M N O P Q R S X Y Z AA AB AC AD AE AF AG AH AI
Seasonal Factors
Normalized Data
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 26.5 29.1 29.9 34.2 33.2 39.6 38.3 58.1 46.4 35.6 33.2 24.7 22.0 20.7 24.5 31.2 0.0
Feb 23.5 28.5 27.5 30.6 33.0 37.5 40.0 47.0 54.6 35.5 31.8 24.4 22.2 22.1 23.2 30.9 0.0
Mar 26.2 27.8 29.9 30.7 35.6 35.9 43.9 55.7 61.8 33.2 31.9 24.8 22.4 22.1 24.1 28.4 0.0
Apr 26.8 27.2 29.6 31.9 35.8 37.2 40.2 43.9 53.5 41.0 27.8 24.6 22.2 21.8 22.6 25.7 0.0
May 23.2 25.6 31.0 31.5 32.2 41.5 41.3 42.5 52.6 54.4 28.5 26.4 21.9 19.4 21.8 25.6 0.0
Jun 24.3 32.8 31.5 27.1 32.1 41.4 45.0 50.5 43.7 43.5 30.0 26.4 26.0 21.1 24.6 28.3 0.0
Jul 24.9 40.5 30.2 29.3 31.5 38.7 49.0 60.5 38.4 36.5 27.3 24.5 20.5 19.2 23.0 23.2 0.0
Aug 21.4 28.0 25.1 25.9 30.6 33.3 55.4 44.6 41.2 32.0 43.6 20.2 19.1 17.8 27.5 21.1 0.0
Sep 35.1 29.2 29.7 27.7 36.1 37.3 40.3 70.1 42.8 32.2 35.0 23.9 21.8 21.4 27.8 25.1 0.0
Oct 27.7 34.7 30.0 32.9 40.7 39.1 41.6 75.7 41.4 33.9 34.5 20.2 20.8 26.7 26.4 23.0 0.0
Nov 27.1 31.2 27.8 32.4 36.4 40.4 52.2 57.3 35.2 33.9 29.6 23.1 20.3 22.4 25.2 27.7 0.0
Dec 29.5 29.5 29.6 35.2 36.8 38.2 44.1 50.2 38.1 33.7 27.6 24.7 23.0 27.6 28.9 25.0 0.0
Growth Rate (Monthly Basis)
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Feb 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 2.0%
Mar 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Apr 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
May 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Jun 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Jul 0.2% 10.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Aug 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Sep 30.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Oct -19.9% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0%
Nov 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0%
Dec 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0%
Cumulative Growth Rate
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Feb 0.3% 0.3% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 2.0%
Mar 0.5% 0.5% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 2.0%
Apr 0.7% 0.7% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 2.0%
May 0.8% 0.8% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 2.0%
Jun 1.0% 1.0% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 2.0%
Jul 1.2% 11.2% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 2.0%
Aug 1.3% 11.3% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 2.0%
Sep 32.0% 11.4% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 2.0%
Oct 5.7% 11.5% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 2.0%
Nov 5.9% 11.6% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.8% 2.0%
Dec 6.1% 11.7% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.8% 2.0%
Avg 4.6% 6.0% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 1.8%
Indexed Cumulative Growth
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 0.96 0.94 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.98
Feb 0.96 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Mar 0.96 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Apr 0.96 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
May 0.96 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Jun 0.97 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Jul 0.97 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Aug 0.97 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Sep 1.26 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Oct 1.01 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Nov 1.01 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Dec 1.01 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Avg 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
Growth-Adjusted Normalized Data
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 27.7 30.7 30.1 34.3 33.3 39.8 38.5 58.3 46.7 35.8 33.3 24.8 22.1 20.8 24.6 31.3 0.0
Feb 24.5 30.1 27.6 30.7 33.1 37.6 40.1 47.2 54.8 35.6 31.9 24.5 22.3 22.2 23.3 31.0 0.0
Mar 27.3 29.3 30.0 30.8 35.7 36.0 44.0 55.9 61.9 33.3 32.0 24.9 22.4 22.1 24.2 28.4 0.0
Apr 27.9 28.7 29.7 32.0 35.9 37.2 40.3 44.0 53.6 41.1 27.9 24.6 22.2 21.8 22.6 25.8 0.0
May 24.1 26.9 31.0 31.5 32.2 41.5 41.4 42.6 52.6 54.5 28.6 26.4 21.9 19.4 21.9 25.6 0.0
Jun 25.2 34.4 31.5 27.2 32.1 41.5 45.1 50.6 43.7 43.6 30.0 26.4 26.0 21.1 24.6 28.3 0.0
Jul 25.7 38.6 30.2 29.3 31.5 38.6 49.0 60.4 38.4 36.5 27.2 24.5 20.5 19.2 23.0 23.2 0.0
Aug 22.1 26.7 25.1 25.9 30.6 33.2 55.4 44.6 41.1 32.0 43.6 20.2 19.0 17.8 27.4 21.1 0.0
Sep 27.8 27.8 29.7 27.6 36.0 37.2 40.2 70.0 42.7 32.1 34.9 23.9 21.7 21.3 27.8 25.0 0.0
Oct 27.4 33.0 29.9 32.8 40.6 39.0 41.5 75.5 41.2 33.8 34.4 20.2 20.7 26.6 26.4 22.9 0.0
Nov 26.7 29.7 27.7 32.3 36.3 40.3 52.0 57.1 35.0 33.7 29.5 23.0 20.3 22.3 25.1 27.6 0.0
Dec 29.1 28.0 29.5 35.0 36.7 38.0 43.9 50.0 37.9 33.6 27.5 24.6 22.9 27.5 28.7 24.9 0.0
Avg 26.3 30.3 29.3 30.8 34.5 38.3 44.3 54.7 45.8 37.1 31.7 24.0 21.8 21.8 25.0 26.3 0.0
0.2% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%
Growth-Adjusted Normalized Data: Factored Max Permitted Standard Deviations: 2.0
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Avg Std Dev Low High Wtd Avg
Jan 1.05 1.01 1.03 1.11 0.97 1.04 0.87 1.07 1.02 0.96 1.05 1.03 1.01 0.95 0.98 1.19 1.02 0.07 0.88 1.17 1.03
Feb 0.93 0.99 0.94 1.00 0.96 0.98 0.91 0.86 1.20 0.96 1.01 1.02 1.02 1.02 0.93 1.18 0.99 0.09 0.82 1.17 0.97
Mar 1.04 0.97 1.02 1.00 1.03 0.94 0.99 1.02 1.35 0.90 1.01 1.04 1.03 1.01 0.97 1.08 1.03 0.10 0.83 1.22 1.01
Apr 1.06 0.95 1.01 1.04 1.04 0.97 0.91 0.81 1.17 1.11 0.88 1.03 1.02 1.00 0.91 0.98 0.99 0.09 0.81 1.17 1.01
May 0.91 0.89 1.06 1.02 0.93 1.08 0.93 0.78 1.15 1.47 0.90 1.10 1.00 0.89 0.88 0.98 1.00 0.16 0.68 1.32 1.00
Jun 0.96 1.13 1.07 0.88 0.93 1.08 1.02 0.92 0.95 1.17 0.95 1.10 1.19 0.97 0.99 1.08 1.02 0.10 0.83 1.21 1.02
Jul 0.98 1.27 1.03 0.95 0.91 1.01 1.11 1.11 0.84 0.98 0.86 1.02 0.94 0.88 0.92 0.88 0.98 0.11 0.76 1.20 0.97
Aug 0.84 0.88 0.86 0.84 0.89 0.87 1.25 0.82 0.90 0.86 1.37 0.84 0.87 0.81 1.10 0.80 0.92 0.17 0.59 1.26 0.89
Sep 1.06 0.92 1.01 0.90 1.04 0.97 0.91 1.28 0.93 0.87 1.10 0.99 0.99 0.98 1.11 0.95 1.00 0.10 0.80 1.21 1.01
Oct 1.04 1.09 1.02 1.07 1.18 1.02 0.94 1.38 0.90 0.91 1.08 0.84 0.95 1.22 1.06 0.87 1.03 0.14 0.75 1.32 1.02
Nov 1.02 0.98 0.95 1.05 1.05 1.05 1.17 1.04 0.76 0.91 0.93 0.96 0.93 1.02 1.01 1.05 0.99 0.09 0.81 1.17 1.00
Dec 1.11 0.92 1.00 1.14 1.06 0.99 0.99 0.91 0.83 0.90 0.87 1.02 1.05 1.26 1.15 0.95 1.01 0.12 0.78 1.24 1.07
Avg 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.11 0.78 1.22 1.00
Data Accepted?
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Total
Jan 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0
Feb 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0
Mar 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1
Apr 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1
May 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1
Jun 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Jul 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Aug 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1
Sep 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1
Oct 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1
Nov 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1
Dec 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1
OK? 1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 8
Use Std
Dev? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Seasonal
Factor
Weights
1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 0 8
Accepted Range
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Seasonal Factors
Final
Initial
Low
High
1. Introduction
2. Inputs
3. Calc
4. Trend
Model Structure: Seasonal Factors Calculation
Growth-Adjusted Seasonal Factors Model
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
A C D E F G H I J K L M N O P Q R S X
Seasonal Factors
Normalized Data
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 26.5 29.1 29.9 34.2 33.2 39.6 38.3 58.1 46.4 35.6 33.2 24.7 22.0 20.7 24.5 31.2 0.0
Feb 23.5 28.5 27.5 30.6 33.0 37.5 40.0 47.0 54.6 35.5 31.8 24.4 22.2 22.1 23.2 30.9 0.0
Mar 26.2 27.8 29.9 30.7 35.6 35.9 43.9 55.7 61.8 33.2 31.9 24.8 22.4 22.1 24.1 28.4 0.0
Apr 26.8 27.2 29.6 31.9 35.8 37.2 40.2 43.9 53.5 41.0 27.8 24.6 22.2 21.8 22.6 25.7 0.0
May 23.2 25.6 31.0 31.5 32.2 41.5 41.3 42.5 52.6 54.4 28.5 26.4 21.9 19.4 21.8 25.6 0.0
Jun 24.3 32.8 31.5 27.1 32.1 41.4 45.0 50.5 43.7 43.5 30.0 26.4 26.0 21.1 24.6 28.3 0.0
Jul 24.9 40.5 30.2 29.3 31.5 38.7 49.0 60.5 38.4 36.5 27.3 24.5 20.5 19.2 23.0 23.2 0.0
Aug 21.4 28.0 25.1 25.9 30.6 33.3 55.4 44.6 41.2 32.0 43.6 20.2 19.1 17.8 27.5 21.1 0.0
Sep 35.1 29.2 29.7 27.7 36.1 37.3 40.3 70.1 42.8 32.2 35.0 23.9 21.8 21.4 27.8 25.1 0.0
Oct 27.7 34.7 30.0 32.9 40.7 39.1 41.6 75.7 41.4 33.9 34.5 20.2 20.8 26.7 26.4 23.0 0.0
Nov 27.1 31.2 27.8 32.4 36.4 40.4 52.2 57.3 35.2 33.9 29.6 23.1 20.3 22.4 25.2 27.7 0.0
Dec 29.5 29.5 29.6 35.2 36.8 38.2 44.1 50.2 38.1 33.7 27.6 24.7 23.0 27.6 28.9 25.0 0.0
26
We start the seasonal factor calculation procedure by bringing in the
normalized data.
TrendModel: Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
A C D E F G H I J K L M N O P Q R S X
Growth Rate (Monthly Basis)
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Feb 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 2.0%
Mar 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Apr 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
May 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Jun 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Jul 0.2% 10.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Aug 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Sep 30.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Oct -19.9% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0%
Nov 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0%
Dec 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0%
27
To adjust the data for growth, we bring in the estimates for both the growth
rate & events.
TrendModel: Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
A C D E F G H I J K L M N O P Q R S X
Cumulative Growth Rate
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0%
Feb 0.3% 0.3% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 2.0%
Mar 0.5% 0.5% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 2.0%
Apr 0.7% 0.7% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 2.0%
May 0.8% 0.8% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 2.0%
Jun 1.0% 1.0% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 2.0%
Jul 1.2% 11.2% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 2.0%
Aug 1.3% 11.3% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 2.0%
Sep 32.0% 11.4% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 2.0%
Oct 5.7% 11.5% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 2.0%
Nov 5.9% 11.6% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.8% 2.0%
Dec 6.1% 11.7% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.8% 2.0%
Avg 4.6% 6.0% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 1.8%
28
Next, the growth is accumulated over the year.
TrendModel: Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
A C D E F G H I J K L M N O P Q R S X
Indexed Cumulative Growth
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 0.96 0.94 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.98
Feb 0.96 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Mar 0.96 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Apr 0.96 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
May 0.96 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Jun 0.97 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Jul 0.97 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Aug 0.97 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Sep 1.26 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Oct 1.01 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Nov 1.01 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Dec 1.01 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Avg 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
29
The cumulative growth rates are then indexed, giving us the factors we need
to adjust the data for growth and events.
TrendModel: Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
A C D E F G H I J K L M N O P Q R S X
Growth-Adjusted Normalized Data
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 27.7 30.7 30.1 34.3 33.3 39.8 38.5 58.3 46.7 35.8 33.3 24.8 22.1 20.8 24.6 31.3 0.0
Feb 24.5 30.1 27.6 30.7 33.1 37.6 40.1 47.2 54.8 35.6 31.9 24.5 22.3 22.2 23.3 31.0 0.0
Mar 27.3 29.3 30.0 30.8 35.7 36.0 44.0 55.9 61.9 33.3 32.0 24.9 22.4 22.1 24.2 28.4 0.0
Apr 27.9 28.7 29.7 32.0 35.9 37.2 40.3 44.0 53.6 41.1 27.9 24.6 22.2 21.8 22.6 25.8 0.0
May 24.1 26.9 31.0 31.5 32.2 41.5 41.4 42.6 52.6 54.5 28.6 26.4 21.9 19.4 21.9 25.6 0.0
Jun 25.2 34.4 31.5 27.2 32.1 41.5 45.1 50.6 43.7 43.6 30.0 26.4 26.0 21.1 24.6 28.3 0.0
Jul 25.7 38.6 30.2 29.3 31.5 38.6 49.0 60.4 38.4 36.5 27.2 24.5 20.5 19.2 23.0 23.2 0.0
Aug 22.1 26.7 25.1 25.9 30.6 33.2 55.4 44.6 41.1 32.0 43.6 20.2 19.0 17.8 27.4 21.1 0.0
Sep 27.8 27.8 29.7 27.6 36.0 37.2 40.2 70.0 42.7 32.1 34.9 23.9 21.7 21.3 27.8 25.0 0.0
Oct 27.4 33.0 29.9 32.8 40.6 39.0 41.5 75.5 41.2 33.8 34.4 20.2 20.7 26.6 26.4 22.9 0.0
Nov 26.7 29.7 27.7 32.3 36.3 40.3 52.0 57.1 35.0 33.7 29.5 23.0 20.3 22.3 25.1 27.6 0.0
Dec 29.1 28.0 29.5 35.0 36.7 38.0 43.9 50.0 37.9 33.6 27.5 24.6 22.9 27.5 28.7 24.9 0.0
Avg 26.3 30.3 29.3 30.8 34.5 38.3 44.3 54.7 45.8 37.1 31.7 24.0 21.8 21.8 25.0 26.3 0.0
30
The normalized data, from above, is adjusted for growth, using the Indexed
Cumulative Growth.
TrendModel: Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
A C D E F G H I J K L M N O P Q R S X
Growth-Adjusted Normalized Data: Factored Max Permitted Standard Deviations: 2.0
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 1.05 1.01 1.03 1.11 0.97 1.04 0.87 1.07 1.02 0.96 1.05 1.03 1.01 0.95 0.98 1.19
Feb 0.93 0.99 0.94 1.00 0.96 0.98 0.91 0.86 1.20 0.96 1.01 1.02 1.02 1.02 0.93 1.18
Mar 1.04 0.97 1.02 1.00 1.03 0.94 0.99 1.02 1.35 0.90 1.01 1.04 1.03 1.01 0.97 1.08
Apr 1.06 0.95 1.01 1.04 1.04 0.97 0.91 0.81 1.17 1.11 0.88 1.03 1.02 1.00 0.91 0.98
May 0.91 0.89 1.06 1.02 0.93 1.08 0.93 0.78 1.15 1.47 0.90 1.10 1.00 0.89 0.88 0.98
Jun 0.96 1.13 1.07 0.88 0.93 1.08 1.02 0.92 0.95 1.17 0.95 1.10 1.19 0.97 0.99 1.08
Jul 0.98 1.27 1.03 0.95 0.91 1.01 1.11 1.11 0.84 0.98 0.86 1.02 0.94 0.88 0.92 0.88
Aug 0.84 0.88 0.86 0.84 0.89 0.87 1.25 0.82 0.90 0.86 1.37 0.84 0.87 0.81 1.10 0.80
Sep 1.06 0.92 1.01 0.90 1.04 0.97 0.91 1.28 0.93 0.87 1.10 0.99 0.99 0.98 1.11 0.95
Oct 1.04 1.09 1.02 1.07 1.18 1.02 0.94 1.38 0.90 0.91 1.08 0.84 0.95 1.22 1.06 0.87
Nov 1.02 0.98 0.95 1.05 1.05 1.05 1.17 1.04 0.76 0.91 0.93 0.96 0.93 1.02 1.01 1.05
Dec 1.11 0.92 1.00 1.14 1.06 0.99 0.99 0.91 0.83 0.90 0.87 1.02 1.05 1.26 1.15 0.95
Avg 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
31
The growth-adjusted data is then expressed as an index.
TrendModel: Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
A C D E F G H I J K L M N O P Q R S X Y Z AA AB AC
Growth-Adjusted Normalized Data: Factored Max Permitted Standard Deviations: 2.0
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Avg Std Dev Low High Wtd Avg
Jan 1.05 1.01 1.03 1.11 0.97 1.04 0.87 1.07 1.02 0.96 1.05 1.03 1.01 0.95 0.98 1.19 1.02 0.07 0.88 1.17 1.03
Feb 0.93 0.99 0.94 1.00 0.96 0.98 0.91 0.86 1.20 0.96 1.01 1.02 1.02 1.02 0.93 1.18 0.99 0.09 0.82 1.17 0.97
Mar 1.04 0.97 1.02 1.00 1.03 0.94 0.99 1.02 1.35 0.90 1.01 1.04 1.03 1.01 0.97 1.08 1.03 0.10 0.83 1.22 1.01
Apr 1.06 0.95 1.01 1.04 1.04 0.97 0.91 0.81 1.17 1.11 0.88 1.03 1.02 1.00 0.91 0.98 0.99 0.09 0.81 1.17 1.01
May 0.91 0.89 1.06 1.02 0.93 1.08 0.93 0.78 1.15 1.47 0.90 1.10 1.00 0.89 0.88 0.98 1.00 0.16 0.68 1.32 1.00
Jun 0.96 1.13 1.07 0.88 0.93 1.08 1.02 0.92 0.95 1.17 0.95 1.10 1.19 0.97 0.99 1.08 1.02 0.10 0.83 1.21 1.02
Jul 0.98 1.27 1.03 0.95 0.91 1.01 1.11 1.11 0.84 0.98 0.86 1.02 0.94 0.88 0.92 0.88 0.98 0.11 0.76 1.20 0.97
Aug 0.84 0.88 0.86 0.84 0.89 0.87 1.25 0.82 0.90 0.86 1.37 0.84 0.87 0.81 1.10 0.80 0.92 0.17 0.59 1.26 0.89
Sep 1.06 0.92 1.01 0.90 1.04 0.97 0.91 1.28 0.93 0.87 1.10 0.99 0.99 0.98 1.11 0.95 1.00 0.10 0.80 1.21 1.01
Oct 1.04 1.09 1.02 1.07 1.18 1.02 0.94 1.38 0.90 0.91 1.08 0.84 0.95 1.22 1.06 0.87 1.03 0.14 0.75 1.32 1.02
Nov 1.02 0.98 0.95 1.05 1.05 1.05 1.17 1.04 0.76 0.91 0.93 0.96 0.93 1.02 1.01 1.05 0.99 0.09 0.81 1.17 1.00
Dec 1.11 0.92 1.00 1.14 1.06 0.99 0.99 0.91 0.83 0.90 0.87 1.02 1.05 1.26 1.15 0.95 1.01 0.12 0.78 1.24 1.07
Avg 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.11 0.78 1.22 1.00
Accepted Range
32
In order to determine what years we wish to exclude, each month’s factors
are averaged, and an acceptable low & high range is calculated.
TrendModel: Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
A C D E F G H I J K L M N O P Q R S X Y Z AA AB AC
Growth-Adjusted Normalized Data: Factored Max Permitted Standard Deviations: 2.0
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Avg Std Dev Low High Wtd Avg
Jan 1.05 1.01 1.03 1.11 0.97 1.04 0.87 1.07 1.02 0.96 1.05 1.03 1.01 0.95 0.98 1.19 1.02 0.07 0.88 1.17 1.03
Feb 0.93 0.99 0.94 1.00 0.96 0.98 0.91 0.86 1.20 0.96 1.01 1.02 1.02 1.02 0.93 1.18 0.99 0.09 0.82 1.17 0.97
Mar 1.04 0.97 1.02 1.00 1.03 0.94 0.99 1.02 1.35 0.90 1.01 1.04 1.03 1.01 0.97 1.08 1.03 0.10 0.83 1.22 1.01
Apr 1.06 0.95 1.01 1.04 1.04 0.97 0.91 0.81 1.17 1.11 0.88 1.03 1.02 1.00 0.91 0.98 0.99 0.09 0.81 1.17 1.01
May 0.91 0.89 1.06 1.02 0.93 1.08 0.93 0.78 1.15 1.47 0.90 1.10 1.00 0.89 0.88 0.98 1.00 0.16 0.68 1.32 1.00
Jun 0.96 1.13 1.07 0.88 0.93 1.08 1.02 0.92 0.95 1.17 0.95 1.10 1.19 0.97 0.99 1.08 1.02 0.10 0.83 1.21 1.02
Jul 0.98 1.27 1.03 0.95 0.91 1.01 1.11 1.11 0.84 0.98 0.86 1.02 0.94 0.88 0.92 0.88 0.98 0.11 0.76 1.20 0.97
Aug 0.84 0.88 0.86 0.84 0.89 0.87 1.25 0.82 0.90 0.86 1.37 0.84 0.87 0.81 1.10 0.80 0.92 0.17 0.59 1.26 0.89
Sep 1.06 0.92 1.01 0.90 1.04 0.97 0.91 1.28 0.93 0.87 1.10 0.99 0.99 0.98 1.11 0.95 1.00 0.10 0.80 1.21 1.01
Oct 1.04 1.09 1.02 1.07 1.18 1.02 0.94 1.38 0.90 0.91 1.08 0.84 0.95 1.22 1.06 0.87 1.03 0.14 0.75 1.32 1.02
Nov 1.02 0.98 0.95 1.05 1.05 1.05 1.17 1.04 0.76 0.91 0.93 0.96 0.93 1.02 1.01 1.05 0.99 0.09 0.81 1.17 1.00
Dec 1.11 0.92 1.00 1.14 1.06 0.99 0.99 0.91 0.83 0.90 0.87 1.02 1.05 1.26 1.15 0.95 1.01 0.12 0.78 1.24 1.07
Avg 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.11 0.78 1.22 1.00
Data Accepted?
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Total
Jan 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0
Feb 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0
Mar 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1
Apr 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1
May 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1
Jun 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Jul 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Aug 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1
Sep 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1
Oct 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1
Nov 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1
Dec 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1
OK? 1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 8
Use Std
Dev? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Seasonal
Factor
Weights
1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 0 8
Accepted Range
33
A “Data Accepted?” table is added that flushes out those years where one or
more months fall outside the accepted range.
TrendModel: Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
A C D E F G H I J K L M N O P Q R S X Y Z AA AB AC
Growth-Adjusted Normalized Data: Factored Max Permitted Standard Deviations: 2.0
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Avg Std Dev Low High Wtd Avg
Jan 1.05 1.01 1.03 1.11 0.97 1.04 0.87 1.07 1.02 0.96 1.05 1.03 1.01 0.95 0.98 1.19 1.02 0.07 0.88 1.17 1.03
Feb 0.93 0.99 0.94 1.00 0.96 0.98 0.91 0.86 1.20 0.96 1.01 1.02 1.02 1.02 0.93 1.18 0.99 0.09 0.82 1.17 0.97
Mar 1.04 0.97 1.02 1.00 1.03 0.94 0.99 1.02 1.35 0.90 1.01 1.04 1.03 1.01 0.97 1.08 1.03 0.10 0.83 1.22 1.01
Apr 1.06 0.95 1.01 1.04 1.04 0.97 0.91 0.81 1.17 1.11 0.88 1.03 1.02 1.00 0.91 0.98 0.99 0.09 0.81 1.17 1.01
May 0.91 0.89 1.06 1.02 0.93 1.08 0.93 0.78 1.15 1.47 0.90 1.10 1.00 0.89 0.88 0.98 1.00 0.16 0.68 1.32 1.00
Jun 0.96 1.13 1.07 0.88 0.93 1.08 1.02 0.92 0.95 1.17 0.95 1.10 1.19 0.97 0.99 1.08 1.02 0.10 0.83 1.21 1.02
Jul 0.98 1.27 1.03 0.95 0.91 1.01 1.11 1.11 0.84 0.98 0.86 1.02 0.94 0.88 0.92 0.88 0.98 0.11 0.76 1.20 0.97
Aug 0.84 0.88 0.86 0.84 0.89 0.87 1.25 0.82 0.90 0.86 1.37 0.84 0.87 0.81 1.10 0.80 0.92 0.17 0.59 1.26 0.89
Sep 1.06 0.92 1.01 0.90 1.04 0.97 0.91 1.28 0.93 0.87 1.10 0.99 0.99 0.98 1.11 0.95 1.00 0.10 0.80 1.21 1.01
Oct 1.04 1.09 1.02 1.07 1.18 1.02 0.94 1.38 0.90 0.91 1.08 0.84 0.95 1.22 1.06 0.87 1.03 0.14 0.75 1.32 1.02
Nov 1.02 0.98 0.95 1.05 1.05 1.05 1.17 1.04 0.76 0.91 0.93 0.96 0.93 1.02 1.01 1.05 0.99 0.09 0.81 1.17 1.00
Dec 1.11 0.92 1.00 1.14 1.06 0.99 0.99 0.91 0.83 0.90 0.87 1.02 1.05 1.26 1.15 0.95 1.01 0.12 0.78 1.24 1.07
Avg 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.11 0.78 1.22 1.00
Data Accepted?
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Total
Jan 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0
Feb 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0
Mar 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1
Apr 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1
May 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1
Jun 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Jul 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Aug 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1
Sep 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1
Oct 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1
Nov 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1
Dec 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1
OK? 1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 8
Use Std
Dev? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Seasonal
Factor
Weights
1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 0 8
Accepted Range
34
A weighted average is calculated, picking up all the accepted years. This is our
goal: the growth-adjusted seasonal factors.
TrendModel: Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
1
2
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
A F G H I
Key Inputs
None Initial
Growth-
Adjusted
Jan-01 1.00 1.00 1.03
Feb-01 1.00 0.96 0.97
Mar-01 1.00 1.00 1.01
Apr-01 1.00 0.99 1.01
May-01 1.00 0.99 1.00
Jun-01 1.00 1.02 1.02
Jul-01 1.00 0.98 0.97
Aug-01 1.00 0.93 0.89
Sep-01 1.00 1.00 1.01
Oct-01 1.00 1.02 1.02
Nov-01 1.00 1.03 1.00
Dec-01 1.00 1.07 1.07
Jan-02
Seasonal Factors
1
2
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
A G H I J
Calculations
B. Seasonally-Adjusted Da
In Use (1 = None; 2 = Initial; 3 = Final) : 2
None Initial "Final" In Use
Jan-01 1.00 1.00 1.03 1.00
Feb-01 1.00 0.96 0.97 0.96
Mar-01 1.00 1.00 1.01 1.00
Apr-01 1.00 0.99 1.01 0.99
May-01 1.00 0.99 1.00 0.99
Jun-01 1.00 1.02 1.02 1.02
Jul-01 1.00 0.98 0.97 0.98
Aug-01 1.00 0.93 0.89 0.93
Sep-01 1.00 1.00 1.01 1.00
Oct-01 1.00 1.02 1.02 1.02
Nov-01 1.00 1.03 1.00 1.03
Dec-01 1.00 1.07 1.07 1.07
Seasonal Factors
1
195
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
A X Y Z AA AB AC
Estimating Trend
Growth-Adjusted Normalized Data: Factored
Avg Std Dev Low High Wtd Avg
Jan 1.02 0.07 0.88 1.17 1.03
Feb 0.99 0.09 0.82 1.17 0.97
Mar 1.03 0.10 0.83 1.22 1.01
Apr 0.99 0.09 0.81 1.17 1.01
May 1.00 0.16 0.68 1.32 1.00
Jun 1.02 0.10 0.83 1.21 1.02
Jul 0.98 0.11 0.76 1.20 0.97
Aug 0.92 0.17 0.59 1.26 0.89
Sep 1.00 0.10 0.80 1.21 1.01
Oct 1.03 0.14 0.75 1.32 1.02
Nov 0.99 0.09 0.81 1.17 1.00
Dec 1.01 0.12 0.78 1.24 1.07
Avg 1.00 0.11 0.78 1.22 1.00
Growth-Adjusted Seasonal Factors Model
35
Note that these final growth-adjusted seasonal factors are the set that are
picked up in both the “Inputs” tab and “Calc” tab.
TrendModel: Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
TrendModel: Inputs
TrendModel: Calc
Growth-Adjusted Seasonal Factors Model
36
We now turn to the chart that will be used to track our estimation of trend.
TrendModel: Trend
1
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
49
50
51
52
53
54
55
56
57
58
59
60
61
62
Y Z AA AB AC AD AE AF AG AH AI AJ
Seasonal Factors In Use: Initial 2
(1 = None; 2 = Initial; 3 = Final)
022.0
24.0
26.0
28.0
30.0
32.0
34.0
36.0
38.0
40.0
Jan-01 Jan-02 Jan-03 Jan-04 Jan-05
Sales
Volumes
(Billions)
NYSE Monthly Sales Volumes
Seasonally-Adjusted
Actual (& Extrapolated) Values
Seasonally-Adjusted: Monthly
Seasonally-Adjusted: 3-Mo Avg
Estimated (& Extrapolated) Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
Model Structure: Chart
Growth-Adjusted Seasonal Factors Model
37
One of the most important aspects for trending the data is the choice of
seasonal factors to use.
TrendModel: Trend
1
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
49
50
51
52
53
54
55
56
57
58
59
60
61
62
Y Z AA AB AC AD AE AF AG AH AI AJ
Seasonal Factors In Use: Initial 2
(1 = None; 2 = Initial; 3 = Final)
22.024.026.028.030.032.034.036.038.040.0S
N
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
38
Focusing on the chart, we start by setting the time range to the 1st three-four
years of the series.
TrendModel: Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
39
Focusing on the chart, we start by setting the time range to the 1st three-four
years of the series.
TrendModel: Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
40
The Actuals are the first set of data to chart. They are colored light gray to de-
emphasize them; they’re here as an FYI.
TrendModel: Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
41
A dotted blue line is added, showing the seasonally-adjusted data.
TrendModel: Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
42
A thicker and solid blue line is added for the 3-month moving average on the
seasonally-adjusted data.
TrendModel: Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
43
Finally, the Estimated Trend line is added to the chart, colored in red to
emphasize its distinction.
TrendModel: Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors Model
44
The heart of the estimation trend analysis is performed at the top of the
“Trend” tab.
TrendModel: Trend
1
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
49
50
51
52
53
54
55
56
57
58
59
60
61
62
A C D E F G H I J K L M N O P Q R S X Y Z AA AB AC AD AE AF AG AH AI AJ
Estimating Trend Seasonal Factors In Use: Initial 2
(1 = None; 2 = Initial; 3 = Final)
Growth Rate
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Feb 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Mar 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Apr 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
May 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Jun 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Jul 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Aug 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Sep 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0%
Oct 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0%
Nov 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0%
Dec 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0%
Start
25.0
Events
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Jan
Feb 2.0%
Mar
Apr
May
Jun
Jul 10.0%
Aug
Sep 30.0%
Oct -20.0%
Nov
Dec
Actuals vs Estimate by Year
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Actual 307.5 363.1 352.4 369.6 415.1 458.5 532.0 660.3 549.3 444.7 383.9 286.8 260.7 261.9 299.1 315.5 0.0
Est 306.4 336.0 357.3 361.9 365.6 366.9 371.3 376.8 378.9 382.9 387.9 389.9 393.1 398.7 402.4 407.4 413.8
Diff -1.1 -27.1 4.9 -7.7 -49.4 -91.6 -160.8 -283.5 -170.4 -61.8 4.1 103.1 132.4 136.8 103.3 91.9
% Diff -0.3% -7.5% 1.4% -2.1% -11.9% -20.0% -30.2% -42.9% -31.0% -13.9% 1.1% 35.9% 50.8% 52.2% 34.5% 29.1%
Total
2001-16 YTD
Actual 6,260 315.5
Est 5,983 407.4
Diff (277) 91.9
% Diff -4.4% 29.1%
022.0
24.0
26.0
28.0
30.0
32.0
34.0
36.0
38.0
40.0
Jan-01 Jan-02 Jan-03 Jan-04 Jan-05
Sales
Volumes
(Billions)
NYSE Monthly Sales Volumes
Seasonally-Adjusted
Actual (& Extrapolated) Values
Seasonally-Adjusted: Monthly
Seasonally-Adjusted: 3-Mo Avg
Estimated (& Extrapolated) Trend
1. Introduction
2. Inputs
3. Calc
4. Trend
Growth-Adjusted Seasonal Factors
45
We now start the process of estimating trend, using a chart and table that
focuses on 3-4 years of time.
1. Introduction
2. Model Structure
3. Estimating Trend
4. Modifying Trend
5. Final Notes
TrendModel: TrendEstimating Trend
1
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
49
50
51
52
53
54
55
56
57
58
59
60
61
62
A C D E F X Y Z AA AB AC AD AE AF AG AH AI AJ
Estimating Trend Seasonal Factors In Use: Initial 2
(1 = None; 2 = Initial; 3 = Final)
Growth Rate
2001 2002 2003 2004
Jan 2.0% 2.0% 1.0% 1.0%
Feb 2.0% 2.0% 1.0% 1.0%
Mar 2.0% 2.0% 1.0% 1.0%
Apr 2.0% 2.0% 1.0% 1.0%
May 2.0% 2.0% 1.0% 1.0%
Jun 2.0% 2.0% 1.0% 1.0%
Jul 2.0% 1.0% 1.0% 1.0%
Aug 2.0% 1.0% 1.0% 1.0%
Sep 2.0% 1.0% 1.0% 1.0%
Oct 2.0% 1.0% 1.0% 1.0%
Nov 2.0% 1.0% 1.0% 1.0%
Dec 2.0% 1.0% 1.0% 1.0%
Start
25.0
Events
2001 2002 2003 2004
Jan
Feb
Mar
Apr
May
Jun
Jul 10.0%
Aug
Sep 30.0%
Oct -20.0%
Nov
Dec
Actuals vs Estimate by Year
2001 2002 2003 2004
Actual 307.5 363.1 352.4 369.6
Est 306.4 336.0 357.3 361.9
Diff -1.1 -27.1 4.9 -7.7
% Diff -0.3% -7.5% 1.4% -2.1%
022.0
24.0
26.0
28.0
30.0
32.0
34.0
36.0
38.0
40.0
Jan-01 Jan-02 Jan-03 Jan-04 Jan-05
Sales
Volumes
(Billions)
NYSE Monthly Sales Volumes
Seasonally-Adjusted
Actual (& Extrapolated) Values
Seasonally-Adjusted: Monthly
Seasonally-Adjusted: 3-Mo Avg
Estimated (& Extrapolated) Trend
Chapter 6: Seasonal Factors
Growth-Adjusted Method
46
Original
Data Holiday
Factors
Normalized
Data
Seasonal
Factors
(Monthly Factors)
Seasonally-
Adjusted
Data:
Initial
Seasonally-
Adjusted
Data:
Initial
Growth Rate
(Adjustments)
Events
(Adjustments)
Seasonally-
Adjusted
Data:
Final
Equated Day
Factors (Day of Week)
Seasonal Factors: Growth-Adjusted Method
47
In Chapter 5 we developed seasonal factors using a method that relied almost solely on
calculations alone; only a quick review afterwards was needed to help verify reasonableness.
Now we come to developing seasonal factors using the more involved “Growth-Adjusted
Method”. I would generally recommend this method, especially if you’re keen to learn from
your history. This method will enable you to:
1. Measure impact of marketing campaigns.
2. Develop alternative estimates that may support other estimates using different approaches:
if the different methods arrive at the same result, much confidence is gained; if results
differ, you have reason to research why – and learn from it.
3. Measure impact of new product launch – on total sales, and on sales of existing products.
4. Estimate price elasticity.
5. Identify and quantify shifts soon after they occur.
Introduction
Seasonal Factors: Growth-Adjusted Method
48
This is a fundamental and critical question. The idea behind “seasonal factors” is that they measure
predictable variability across the year, based entirely on the time of year alone. We want to know how
much busier or quieter a metric will be during April or October solely because it is April or October.
Business variability due to the length of the month was addressed by normalizing the data. We wish to
answer the question: all else being equal (price levels, product availability, general economy, weather, etc.),
how much busier or quieter is it because it’s April or October?
To illustrate, suppose you have a business with constant growth, like the 10% annual rate of growth
depicted in Chart 6.1? If we take the data “as is”, without adjusting for growth, we will have seasonal
factors looking like those in Chart 6.2, which shows December is almost 9% busier than January.
Why Adjust for Growth?
1. Construct “Inputs” tab
2. Construct “Calc” tab
3. Construct “Trend” tab
4. Run Preliminary Trend
5. Run Final Trend
Chart 6.1: XYZ’s Constant Growth Chart 6.2: XYZ’s Seasonal Factors
It may be difficult to
make out from the
chart, but all 4 years
have the same
identical pattern.
Seasonal Factors: Growth-Adjusted Method
49
Were we to apply these seasonal factors to the original data, with January numbers increased
and December numbers decreased, we arrive at the series of step functions displayed in Chart
6.3. Seasonally-adjusting the data has stripped out all the growth, resulting in a pattern of flat
growth punctuated by 10% bumps every January. Its pretty apparent that seasonalizing the
data here gives us a false picture of how business is behaving. Growth should be constant, not
flat; the problem is that the seasonal factors include the growth.
In order for the seasonally-adjusted data to capture correctly the “true” pattern of consistent
growth we need to make sure we adjust for growth when developing the seasonal factors. In
effect, we want the seasonal factors to look like the dotted bold green line in Chart 6.4.
Why Adjust for Growth? (cont.)
1. Construct “Inputs” tab
2. Construct “Calc” tab
3. Construct “Trend” tab
4. Run Preliminary Trend
5. Run Final Trend
Chart 6.4: XYZ’s “True” Seasonal FactorsChart 6.3: XYZ Sales, Seasonally-Adjusted
Seasonal Factors: Growth-Adjusted Method
50
When our seasonal factors are adjusted for growth, resulting here in a flat “zero” seasonality,
we end up with a seasonally-adjusted line in Chart 6.5 that is identical to the original data.
This is as it should be for as constructed in our idealized original, there is no seasonality, there
is no pattern of consistent fluctuation across the year.
1. Construct “Inputs” tab
2. Construct “Calc” tab
3. Construct “Trend” tab
4. Run Preliminary Trend
5. Run Final Trend
Chart 6.5: XYZ Sales, Seasonally-Adjusted
Obviously, data never behaves so smoothly and
“perfectly” as this. We simplified it to illustrate
an essential point: when data is not adjusted
for growth, the consequent seasonal factors
that are developed will fail to capture the
pattern across the year that is solely due to
seasonality alone; instead it will mistakenly
include growth, and thereby distort how the
underlying data is truly behaving.
If growth was an absolute constant, that
wouldn’t be a problem; but that is rarely, if
ever, the case.
Why Adjust for Growth? (cont.)
51
The basic approach for the Growth-Adjusted Method involves five main steps:
1. Start with normalized data (already adjusted for calendar effect).
2. Estimate growth rates and events over the given period.
3. Calculate the cumulative growth rate by month, including events.
4. Adjust the normalized data for the cumulative growth, and express as an index.
5. Calculate standard deviations, and remove outlier data.
Approach
No. Action Description
1 Construct “Input” section “Input” tab collects key data from outside sources; it can be easily updated.
2 Construct “Calc” section “Calc” tab is where almost the calculations for the model are performed.
3 Construct “Trend” section Basic framework is established for trending the data, including chart.
4 Run Preliminary Trend A first set of trend estimates are manually input into “Trend” tab.
5 Run Final Trend
Model is updated to use the model’s estimate of seasonal factors; the trend
estimates are tweaked using the new & improved factors.
This Growth-Adjusted technique is described in detail in
Appendix C, How to Develop Growth-Adjusted Seasonal Factors.
Look to this appendix for explanation of the how and why these
factors can be developed. In these summary pages, we will
highlight the main features and process.
Seasonal Factors: Growth-Adjusted Method
1
2
7
8
9
10
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
609
610
611
612
613
614
615
616
617
618
619
620
621
622
A B C D E
Key Inputs
Linked to diff file
Avg Days per Mo (1970-97): 20.73
Avg Days per Mo (1998-2020): 20.69
Actuals
No. of
Days
Norm
Factor
Seas Factor
(Short Method)
Jan-00 21,484,254,618 20.4 0.99 1.02
Feb-00 20,917,632,140 19.8 0.96 0.99
Mar-00 26,182,766,564 23.1 1.12 1.00
Apr-00 20,140,405,405 18.9 0.91 0.99
May-00 19,919,341,288 21.7 1.05 0.99
Jun-00 21,703,321,017 22.1 1.07 1.02
Jul-00 19,076,891,454 19.1 0.92 0.96
Aug-00 20,379,201,651 23.1 1.12 0.88
Sep-00 20,825,856,353 19.8 0.96 1.00
Oct-00 25,972,211,976 21.6 1.04 1.07
Nov-00 21,700,515,606 20.4 0.98 1.00
Dec-00 24,175,307,011 18.6 0.90 1.07
Jan-01 27,844,005,557 21.9 1.06 1.02
Feb-01 21,631,058,254 18.8 0.91 0.99
Mar-01 27,970,177,009 22.0 1.07 1.00Jan-19 0 21.1 1.02 1.02Feb-19 0 18.8 0.91 0.99Mar-19 0 21.0 1.02 1.00Apr-19 0 20.8 1.01 0.99May-19 0 21.8 1.05 0.99Jun-19 0 20.0 0.97 1.02Jul-19 0 21.2 1.03 0.96Aug-19 0 21.9 1.06 0.88Sep-19 0 19.8 0.96 1.00Oct-19 0 22.7 1.10 1.07
Nov-19 0 19.3 0.93 1.00
Dec-19 0 19.4 0.94 1.07
Jan-20 0 21.3 1.03 1.02
Feb-20 0 18.8 0.91 0.99
Mar-20 0 21.9 1.06 1.00
Apr-20 0 20.9 1.01 0.99
May-20 0 19.7 0.95 0.99
Jun-20 0 22.2 1.07 1.02
Jul-20 0 21.8 1.05 0.96
Aug-20 0 20.9 1.01 0.88
Sep-20 0 20.7 1.00 1.00
Oct-20 0 21.8 1.05 1.07
Nov-20 0 19.2 0.93 1.00
Dec-20 0 20.3 0.98 1.07
Seasonal Factors: Growth-Adjusted Method
52
Table 6.1 captures some of the key pieces of data we
will be using for trending NYSE sales. The Actuals (Col.
B) are captured here, as well as previously developed
month lengths (Col. C) and seasonal factors (Col. E).
Column D calculates the normalization factors,
representing each month’s length as an index, where
the length is compared with the average month length
over the entire period, not just compared to each
individual year’s length. Why? Because some years are
longer or shorter than others due to whether the 365th
day falls on a weekday or weekend, leap year, events –
e.g. the NYSE was closed 4 days after 9/11, 2 days for
Hurricane Sandy, etc.
Construct “Inputs” tab
1. Construct “Inputs” tab
2. Construct “Calc” tab
3. Construct “Trend” tab
4. Run Preliminary Trend
5. Run Final Trend
Table 6.1: Inputs
Inputs
The overall 1970-2020 period is
split in two here because of the
addition of the Martin Luther
King holiday, starting in 1998.
Note that the entire 1970-2020 period was split in
two because the years 1998-on came in slightly
lower than previously, due to the markets being
closed for Martin Luther King Day, starting in 1998.
Also note that 2001 was removed from the 1998-
2020 average calculation: it was the only year that
had so many additional closures - the NYSE was
shut 4 days following the 9/11 attacks.
Seasonal Factors: Growth-Adjusted Method
53
The “Calc” tab is the place where virtually all the calculations are performed. Table 6.2 below
shows the entire set of calculations that we make with the NYSE data. These calculations are
divided into five sections which are fully described in the Appendix. A summary:
Construct “Calc” tab: What Performed Here
1. Construct “Inputs” tab
2. Construct “Calc” tab
3. Construct “Trend” tab
4. Run Preliminary Trend
5. Run Final Trend
Table 6.2: Calc tab
Calc
Section Activity Description
A Actual & Normalized Data Place for manual data adjustments to be inserted (Col. C); adjusted actuals are then normalized (Col. F).
B Seasonally-Adjusted Data
Seasonal factor estimates are brought in – whatever already available (Col. G) and then those to be calculated
in the “Trend” tab (Col. H). Normalized data is then seasonally-adjusted (Col. J), and smoothed (Col. K).
C Estimated Trend
Picks up your estimates of growth & events (Col. L, M) – performed in “Trend” tab; calculates trend using
those estimates (Col. N). “Trend” is the smoothed line; “Values” have the “noise” of calendar & seasonality
put back in.
D Forecasts Calculates forecasts, by growing the prior period trend value using your estimates of “Growth” & “Events”.
E Other Additional miscellaneous calculations that may be useful for reference or charting purposes.
1
2
7
8
9
10
371
372
373
557
558
559
560
561
562
563
564
565
A B C D E F G H I J K L M N O P Q R S T
Calculations Unit: 0.000000001 (Billions)
In Use: 1 Start: 20.000
Actuals
Adjust-
ments
Adjusted
Actuals
Normalization
Factors
Normalized
Data Initial
Growth-
Adjusted In Use
Seasonally-
Adjusted:
Monthly
Seasonally-
Adjusted: 3-
Mo Avg
Growth
Rate
1-Time
Events
Estimated
Trend
Estimated
Trend
Values
Extrapolated
Trend
Extrapolated
Trend Values
(= Forecast)
Estimated (&
Forecast)
Trend
Actual (&
Forecast)
Values
Estimate vs
Actual: Diff
Jan-00 21.484 21.484 0.99 21.754 1.02 0 1.02 21.417 20.577 15.0% 0.0% 20.250 20.313 20.250 21.484 (1.234)
Feb-00 20.918 20.918 0.96 21.874 0.99 0 0.99 22.139 22.304 15.0% 0.0% 20.503 19.372 20.503 20.918 (0.415)
Mar-00 26.183 26.183 1.12 23.452 1.00 0 1.00 23.356 22.559 15.0% 0.0% 20.759 23.272 20.759 26.183 (5.423)Jul-14 20.238 20.238 1.05 19.219 0.96 0 0.96 19.919 20.159 5.0% 0.0% 21.203 21.542 21.203 20.238 0.965Aug-14 17.852 17.852 1.01 17.704 0.88 0 0.88 20.074 20.477 5.0% 0.0% 21.291 18.934 21.291 17.852 3.440Sep-14 21.684 21.684 1.01 21.533 1.00 0 1.00 21.437 22.166 5.0% 5.0% 22.449 22.708 22.449 21.684 0.765Oct-14 29.250 29.250 1.10 26.571 1.06 0 1.06 24.988 22.883 5.0% 0.0% 22.543 26.387 22.543 29.250 (6.707)Nov-14 19.750 19.750 0.88 22.418 1.01 0 1.01 22.224 24.168 5.0% 0.0% 22.637 20.117 22.637 19.750 2.887Dec-14 26.228 26.228 0.98 26.898 1.06 0 1.06 25.291 23.861 5.0% 0.0% 22.731 23.573 22.731 26.228 (3.497)Jan-15 23.907 23.907 0.98 24.447 1.02 0 1.02 24.069 24.403 5.0% 0.0% 22.826 22.672 22.826 23.907 (1.235)Feb-15 21.359 21.359 0.91 23.566 0.99 0 0.99 23.851 23.975 5.0% 0.0% 22.921 20.526 22.921 21.359 (0.833)Mar-15 25.555 25.555 1.06 24.105 1.00 0 1.00 24.007 23.509 5.0% 0.0% 23.016 24.500 23.016 25.555 (1.055)Apr-15 22.758 22.758 1.01 22.522 0.99 0 0.99 22.670 22.925 5.0% 0.0% 23.112 23.201 23.112 22.758 0.444May-15 20.907 20.907 0.95 21.909 0.99 0 0.99 22.098 22.961 5.0% 0.0% 23.208 21.958 23.208 20.907 1.050Jun-15 26.087 26.087 1.06 24.605 1.02 0 1.02 24.116 23.402 5.0% 0.0% 23.305 25.210 23.305 26.087 (0.877)
Jul-15 24.478 24.478 1.06 23.149 0.96 0 0.96 23.992 26.425 5.0% 0.0% 23.402 23.877 23.402 24.478 (0.602)
Aug-15 27.811 27.811 1.01 27.489 0.88 0 0.88 31.168 27.656 5.0% 20.0% 28.200 25.163 28.200 27.811 (2.649)
Sep-15 28.009 28.009 1.00 27.933 1.00 0 1.00 27.808 29.667 5.0% 0.0% 28.317 28.522 28.317 28.009 0.513
Oct-15 33.580 33.580 1.05 31.926 1.06 0 1.06 30.024 28.223 5.0% 0.0% 28.435 31.802 28.435 33.580 (1.778)
Nov-15 25.159 25.159 0.93 27.070 1.01 0 1.01 26.835 28.551 5.0% 0.0% 28.554 26.770 28.554 25.159 1.611
Dec-15 30.015 30.015 0.98 30.621 1.06 0 1.06 28.792 28.526 5.0% 0.0% 28.673 29.891 28.673 30.015 (0.124)
Jan-16 28.688 28.688 0.94 30.422 1.02 0 1.02 29.951 29.372 5.0% 0.0% 28.792 27.578 28.792 28.688 (1.110)
Feb-16 0 0 0.95 0 0.99 0 0.99 5.0% 0.0% 28.912 27.177 28.912 27.177 0
Mar-16 0 0 1.06 0 1.00 0 1.00 5.0% 0.0% 29.033 30.868 29.033 30.868 0
D. Forecasts E. Other
Seasonal Factors
A. Actual & Normalized Data B. Seasonally-Adjusted Data C. Estimated Trend
Seasonal Factors: Growth-Adjusted Method
54
A crucial step in growth-adjusting the data is the insertion of estimates of growth. These
estimates should be broken out into at least two separate groupings: the “Growth Rate” that
captures the underlying longer-term growth (or decline) of the data, and the “Events” that
capture the shifts that periodically occur (& usually constitute most of what is labeled as
“growth”). Table 6.3 illustrates what these look like, with periodic changes in the growth rate
highlighted using conditional formatting, and 1-time event estimates captured in a separate
table (Rows 31-42).
Construct “Trend” tab
1. Construct “Inputs” tab
2. Construct “Calc” tab
3. Construct “Trend” tab
4. Run Preliminary Trend
5. Run Final Trend
The numbers developed here
are illustrative. Accurate
estimation of growth rates
and events is an iterative
process. For now we are
focused on developing
growth-adjusted seasonal
factors (GASF); the values here
will be used to show how we
develop those GASFs.
In the next chapter, we will
turn our attention to
“Estimating Trend” and
specifically developing more
appropriate values than those
shown here.
Table 6.3: Illustration of Growth & Event Estimates
Trend
1
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
A C D E F G H I J K L M N O P Q R S T U
Estimating Trend
Growth Rate
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
Jan 15.0% 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 5.0% 2.0% 0.0%
Feb 15.0% 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 5.0% 2.0% 0.0%
Mar 15.0% 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 5.0% 2.0% 0.0%
Apr 15.0% 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 2.0% 2.0% 0.0%
May 15.0% 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 2.0% 2.0% 0.0%
Jun 15.0% 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 2.0% 2.0% 0.0%
Jul 15.0% 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% 5.0% 5.0% 2.0% 2.0% 0.0%
Aug 15.0% 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% 5.0% 5.0% 2.0% 2.0% 0.0%
Sep 15.0% 15.0% 0.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 5.0% 2.0% 2.0% 0.0%
Oct 15.0% 15.0% 0.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 5.0% 2.0% 2.0% 0.0%
Nov 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 5.0% 2.0% 2.0% 0.0%
Dec 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 5.0% 2.0% 2.0% 0.0%
Start 20.0
1-Time Events
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
Jan
Feb
Mar
Apr -15.0%
May -35.0%
Jun
Jul 10.0%
Aug -15.0% 20.0%
Sep 25.0% 5.0%
Oct
Nov 10.0%
Dec
Conditional formatting
is applied to highlight
when growth rates
(Rows 11-22) change.
Ch 5 final seas factors
Ch 5 final seas factors
Ch 5 final seas factors
Ch 5 final seas factors
Ch 5 final seas factors
Ch 5 final seas factors

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Ch 5 final seas factors

  • 1. Chapter 5: Growth-Adjusted 1 Seasonal Factors Model Original Data Equated Day Factors Holiday Factors Normalized Data Initial Seasonal Factors Seasonally- Adjusted Data: Initial Seasonally- Adjusted Data: Initial Growth Rate (Adjustments) Events (Adjustments) Seasonally- Adjusted Data: Final Growth-Adj Seasonal Factors
  • 2. Growth-Adjusted Seasonal Factors Model 2 This chapter will walk through the model structure that will be used to arrive at the growth-adjusted seasonal factors. 1. Introduction 2. Inputs 3. Calc 4. Trend 1. Introduction – why growth-adjust? 2. Model Structure: Inputs 3. Model Structure: Calc 4. Model Structure: Trend Introduction
  • 3. Growth-Adjusted Seasonal Factors Model Jan Jan Dec Jan Dec Dec Dec is much higher than Jan each year due to GROWTH, not to seasonality. XYZ Sales – with Growth WITH Growth Year 1 Year 2 Year 3 3 Growth is removed so the seasonality measure only captures seasonality, nothing else. 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 4. Growth-Adjusted Seasonal Factors Model Jan Dec Dec is much higher than Jan each year due to GROWTH, not to seasonality. XYZ Sales – with & without Growth WITH Growth WITHOUT Growth Without Growth, the “true” seasonal pattern is more obvious. Year 1 Year 2 Year 3 Jan Dec 4 Removing growth reveals the “true” relationship between January and December (& all other months). 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 5. Growth-Adjusted Seasonal Factors Model Sep Year 1 Year 2 Year 3 Seasonal pattern can be further skewed if Events are included. XYZ Sales – with & without Growth & Events WITH Growth & Event WITHOUT Growth & Event Adjusting for Events as well as Growth reveals seasonal pattern. New product lifts sales in Sep by 15% WITH Growth only 5 Adjustments need to be made for events as well. 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 6. Growth-Adjusted Seasonal Factors Model 6 After adjusting for growth & events, the “true” underlying seasonal pattern emerges. 1. Introduction 2. Inputs 3. Calc 4. Trend Seasonality: Without Growth Adjustment Seasonality: With Growth Adjustment
  • 7. Growth-Adjusted Seasonal Factors Model 7 The Excel model for developing the growth-adjusted seasonal factors, and for estimating trend, has three parts. 1. Data Inputs (“Inputs” tab) 2. Calculations (“Calc” tab) 3. Trend Estimate (“Trend” tab) 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 8. Growth-Adjusted Seasonal Factors Model 8 The “Inputs” tab contains all the key information drawn from other files that will be used to estimate trend. 1 2 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 197 198 199 200 201 202 203 204 249 250 251 279 A B C D E F Key Inputs Linked to diff file Actuals No. of Days Norm Factor Normalized Data Jan-01 27.844 21.7 1.05 26.510 Feb-01 21.631 19.1 0.92 23.459 Mar-01 27.970 22.0 1.07 26.229 Apr-01 25.529 19.7 0.95 26.799 May-01 24.568 21.9 1.06 23.175 Jun-01 24.674 21.0 1.02 24.284 Jul-01 23.878 19.8 0.96 24.883 Aug-01 23.591 22.8 1.10 21.354 Sep-01 25.417 15.0 0.72 35.098 Oct-01 30.229 22.6 1.09 27.692 Nov-01 26.672 20.4 0.99 27.054 Dec-01 25.506 17.8 0.86 29.529 Jan-02 29.943 21.3 1.03 29.056 Feb-02 26.255 19.1 0.92 28.474Jan-16 29.393 19.5 0.94 31.219Feb-16 29.857 20.0 0.97 30.918Mar-16 29.947 21.8 1.06 28.373Apr-16 26.183 21.0 1.02 25.739May-16 25.757 20.8 1.01 25.606Jun-16 30.123 22.0 1.06 28.334 Jul-16 22.328 19.9 0.96 23.217 Aug-16 23.490 23.0 1.11 21.141 Sep-16 25.282 20.8 1.01 25.100 Oct-16 22.795 20.5 0.99 22.964 Nov-16 22.000 20.4 0.99 22.307 Dec-16 22.000 19.0 0.92 23.878 Jan-17 0.000 20.4 0.99 0.000 Feb-17 0.000 19.0 0.92 0.000Jan-20 0.000 21.4 1.03 0.000Feb-20 0.000 19.0 0.92 0.000Mar-20 0.000 21.9 1.06 0.000Apr-20 0.000 20.8 1.01 0.000May-20 0.000 19.8 0.96 0.000Jun-20 0.000 21.9 1.06 0.000Jul-20 0.000 22.0 1.07 0.000Aug-20 0.000 20.9 1.01 0.000Sep-20 0.000 20.8 1.01 0.000Oct-20 0.000 21.6 1.05 0.000 Nov-20 0.000 19.3 0.93 0.000 Dec-20 0.000 19.3 0.94 0.000 Jan-21 0.000 0.0 0.00 0.000 TrendModel: Inputs Update with data thru Dec 2016 1. Introduction 2. Inputs 3. Calc 4. Trend Model Structure: Inputs
  • 9. Growth-Adjusted Seasonal Factors Model 9 The “Inputs” tab also brings in the seasonal factors – the initial factors already developed, and the growth-adjusted factors to be developed in the model. 1 2 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 197 198 199 200 201 202 203 204 249 250 251 279 A B C D E F G H I J Key Inputs Linked to diff file Actuals No. of Days Norm Factor Normalized Data None Initial Growth- Adjusted Jan-01 27.844 21.7 1.05 26.510 1.00 1.00 1.03 Feb-01 21.631 19.1 0.92 23.459 1.00 0.96 0.98 Mar-01 27.970 22.0 1.07 26.229 1.00 1.00 1.01 Apr-01 25.529 19.7 0.95 26.799 1.00 0.99 1.01 May-01 24.568 21.9 1.06 23.175 1.00 0.99 1.00 Jun-01 24.674 21.0 1.02 24.284 1.00 1.02 1.03 Jul-01 23.878 19.8 0.96 24.883 1.00 0.98 0.97 Aug-01 23.591 22.8 1.10 21.354 1.00 0.93 0.89 Sep-01 25.417 15.0 0.72 35.098 1.00 1.00 1.01 Oct-01 30.229 22.6 1.09 27.692 1.00 1.02 1.02 Nov-01 26.672 20.4 0.99 27.054 1.00 1.03 1.00 Dec-01 25.506 17.8 0.86 29.529 1.00 1.07 1.06 Jan-02 29.943 21.3 1.03 29.056 Feb-02 26.255 19.1 0.92 28.474Jan-16 29.393 19.5 0.94 31.219Feb-16 29.857 20.0 0.97 30.918Mar-16 29.947 21.8 1.06 28.373Apr-16 26.183 21.0 1.02 25.739May-16 25.757 20.8 1.01 25.606Jun-16 30.123 22.0 1.06 28.334 Jul-16 22.328 19.9 0.96 23.217 Aug-16 23.490 23.0 1.11 21.141 Sep-16 25.282 20.8 1.01 25.100 Oct-16 22.795 20.5 0.99 22.964 Nov-16 22.000 20.4 0.99 22.307 Dec-16 22.000 19.0 0.92 23.878 Jan-17 0.000 20.4 0.99 0.000 Feb-17 0.000 19.0 0.92 0.000Jan-20 0.000 21.4 1.03 0.000Feb-20 0.000 19.0 0.92 0.000Mar-20 0.000 21.9 1.06 0.000Apr-20 0.000 20.8 1.01 0.000May-20 0.000 19.8 0.96 0.000Jun-20 0.000 21.9 1.06 0.000Jul-20 0.000 22.0 1.07 0.000Aug-20 0.000 20.9 1.01 0.000Sep-20 0.000 20.8 1.01 0.000Oct-20 0.000 21.6 1.05 0.000 Nov-20 0.000 19.3 0.93 0.000 Dec-20 0.000 19.3 0.94 0.000 Jan-21 0.000 0.0 0.00 0.000 Seasonal Factors TrendModel: Inputs Update with data thru Dec 2016 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 10. Growth-Adjusted Seasonal Factors Model 10 The “Calc” tab is where all the calculations are performed. Except for updating monthly data, this tab need never be touched. TrendModel: Calc 1 2 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 197 198 199 200 201 202 203 204 205 A B C D E F G H I J K L M N O P Q R S T U Calculations Unit: 1 In Use (1 = None; 2 = Initial; 3 = Final) : 2 Start: 25.000 Actuals Adjust- ments Adjusted Actuals Normalization Factors Normalized Data None Initial Revised In Use Seasonally- Adjusted: Monthly Seasonally- Adjusted: 3- Mo Avg Growth Rate 1-Time Events Estimated Trend Estimated Trend Values Extrapolated Trend Extrapolated Trend Values (= Forecast) Estimated (& Forecast) Trend Actual (& Forecast) Values Estimate vs Actual: Diff Jan-01 27.844 27.844 1.05 26.510 1.00 1.00 1.03 1.00 26.406 25.412 2.0% 0.0% 25.000 26.362 25.000 27.844 (2.844) Feb-01 21.631 21.631 0.92 23.459 1.00 0.96 0.97 0.96 24.418 25.666 2.0% 0.0% 25.042 22.184 25.042 21.631 3.411 Mar-01 27.970 27.970 1.07 26.229 1.00 1.00 1.01 1.00 26.174 25.849 2.0% 0.0% 25.083 26.805 25.083 27.970 (2.887) Apr-01 25.529 25.529 0.95 26.799 1.00 0.99 1.01 0.99 26.954 25.517 2.0% 0.0% 25.125 23.797 25.125 25.529 (0.404) May-01 24.568 24.568 1.06 23.175 1.00 0.99 1.00 0.99 23.424 24.712 2.0% 0.0% 25.167 26.397 25.167 24.568 0.599 Jun-01 24.674 24.674 1.02 24.284 1.00 1.02 1.02 1.02 23.756 24.153 2.0% 0.0% 25.209 26.183 25.209 24.674 0.535 Jul-01 23.878 23.878 0.96 24.883 1.00 0.98 0.97 0.98 25.279 24.015 2.0% 0.0% 25.251 23.852 25.251 23.878 1.373 Aug-01 23.591 23.591 1.10 21.354 1.00 0.93 0.89 0.93 23.011 27.767 2.0% 0.0% 25.293 25.930 25.293 23.591 1.702 Sep-01 25.417 25.417 0.72 35.098 1.00 1.00 1.01 1.00 35.011 28.406 2.0% 30.0% 32.936 23.911 32.936 25.417 7.519 Oct-01 30.229 30.229 1.09 27.692 1.00 1.02 1.02 1.02 27.195 29.510 2.0% -20.0% 26.393 29.337 26.393 30.229 (3.836) Nov-01 26.672 26.672 0.99 27.054 1.00 1.03 1.00 1.03 26.326 27.069 2.0% 0.0% 26.437 26.784 26.437 26.672 (0.235) Dec-01 25.506 25.506 0.86 29.529 1.00 1.07 1.07 1.07 27.685 27.651 2.0% 0.0% 26.481 24.396 26.481 25.506 0.975 Jan-02 29.943 29.943 1.03 29.056 1.00 1.00 1.03 1.00 28.941 28.754 2.0% 0.0% 26.525 27.443 26.525 29.943 (3.418)Feb-02 26.255 26.255 0.92 28.474 1.00 0.96 0.97 0.96 29.637 28.775 2.0% 0.0% 26.569 23.537 26.569 26.255 0.314Mar-02 26.743 26.743 0.96 27.806 1.00 1.00 1.01 1.00 27.747 28.260 2.0% 0.0% 26.613 25.650 26.613 26.743 (0.130)Apr-02 28.761 28.761 1.06 27.239 1.00 0.99 1.01 0.99 27.397 27.017 2.0% 0.0% 26.658 27.985 26.658 28.761 (2.103)May-02 27.152 27.152 1.06 25.632 1.00 0.99 1.00 0.99 25.908 28.461 2.0% 0.0% 26.702 27.984 26.702 27.152 (0.450)Jun-02 31.740 31.740 0.97 32.791 1.00 1.02 1.02 1.02 32.079 33.049 2.0% 0.0% 26.747 26.464 26.747 31.740 (4.993)Jul-02 41.499 41.499 1.02 40.516 1.00 0.98 0.97 0.98 41.160 34.472 1.0% 0.0% 26.769 26.989 26.769 41.499 (14.730)Aug-02 29.511 29.511 1.05 28.003 1.00 0.93 0.89 0.93 30.177 33.477 1.0% 0.0% 26.791 26.200 26.791 29.511 (2.719)Sep-02 28.180 28.180 0.97 29.168 1.00 1.00 1.01 1.00 29.095 31.102 1.0% 0.0% 26.813 25.971 26.813 28.180 (1.367)Oct-02 38.061 38.061 1.10 34.657 1.00 1.02 1.02 1.02 34.034 31.178 1.0% 0.0% 26.836 30.011 26.836 38.061 (11.225)Nov-02 29.087 29.087 0.93 31.245 1.00 1.03 1.00 1.03 30.404 30.700 1.0% 0.0% 26.858 25.695 26.858 29.087 (2.229)Dec-02 26.205 26.205 0.89 29.503 1.00 1.07 1.07 1.07 27.660 29.293 1.0% 0.0% 26.881 25.466 26.881 26.205 0.676 Jul-16 22.328 22.328 0.96 23.217 1.00 0.98 0.97 0.98 23.585 24.695 1.0% 0.0% 30.790 29.149 30.790 22.328 6.821 Aug-16 23.490 23.490 1.11 21.141 1.00 0.93 0.89 0.93 22.782 23.801 1.0% 0.0% 30.815 31.773 30.815 23.490 8.283 Sep-16 25.282 25.282 1.01 25.100 1.00 1.00 1.01 1.00 25.037 23.457 1.0% 0.0% 30.841 31.143 30.841 25.282 5.861 Oct-16 22.795 22.795 0.99 22.964 1.00 1.02 1.02 1.02 22.552 24.850 1.0% 0.0% 30.867 31.200 30.867 22.795 8.405 Nov-16 27.327 27.327 0.99 27.708 1.00 1.03 1.00 1.03 26.963 24.306 1.0% 0.0% 30.892 31.310 30.892 27.327 3.983 Dec-16 23.000 23.000 0.92 24.963 1.00 1.07 1.07 1.07 23.404 25.183 1.0% 0.0% 30.918 30.385 30.918 23.000 7.385 Jan-17 0 0 0.99 0 1.00 1.00 1.03 1.00 1.0% 0.0% 30.944 30.666 30.944 30.666 0 Feb-17 0 0 0.92 0 1.00 0.96 0.97 0.96 1.0% 0.0% 30.970 27.396 30.970 27.396 0 Mar-17 0 0 1.12 0 1.00 1.00 1.01 1.00 1.0% 0.0% 30.996 34.673 30.996 34.673 0 E. Estimate & Actual Seasonal Factors A. Actual & Normalized Data B. Seasonally-Adjusted Data C. Estimated Trend D. Forecasts 1. Introduction 2. Inputs 3. Calc 4. Trend Model Structure: Calc
  • 11. Growth-Adjusted Seasonal Factors Model 11 The first part of the “Calc” brings in the original data, allows for adjustments if needed, and calculates the normalized monthly amounts. TrendModel: Calc 1 2 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 197 198 199 200 201 202 203 204 205 A B C D E F Calculations Unit: 1 In Use (1 = None; 2 = Initial; 3 = Final) : Actuals Adjust- ments Adjusted Actuals Normalization Factors Normalized Data Jan-01 27.844 27.844 1.05 26.510 Feb-01 21.631 21.631 0.92 23.459 Mar-01 27.970 27.970 1.07 26.229 Apr-01 25.529 25.529 0.95 26.799 May-01 24.568 24.568 1.06 23.175 Jun-01 24.674 24.674 1.02 24.284 Jul-01 23.878 23.878 0.96 24.883 Aug-01 23.591 23.591 1.10 21.354 Sep-01 25.417 25.417 0.72 35.098 Oct-01 30.229 30.229 1.09 27.692 Nov-01 26.672 26.672 0.99 27.054 Dec-01 25.506 25.506 0.86 29.529 Jan-02 29.943 29.943 1.03 29.056Feb-02 26.255 26.255 0.92 28.474Mar-02 26.743 26.743 0.96 27.806Apr-02 28.761 28.761 1.06 27.239May-02 27.152 27.152 1.06 25.632Jun-02 31.740 31.740 0.97 32.791Jul-02 41.499 41.499 1.02 40.516Aug-02 29.511 29.511 1.05 28.003Sep-02 28.180 28.180 0.97 29.168Oct-02 38.061 38.061 1.10 34.657Nov-02 29.087 29.087 0.93 31.245Dec-02 26.205 26.205 0.89 29.503 Jul-16 22.328 22.328 0.96 23.217 Aug-16 23.490 23.490 1.11 21.141 Sep-16 25.282 25.282 1.01 25.100 Oct-16 22.795 22.795 0.99 22.964 Nov-16 27.327 27.327 0.99 27.708 Dec-16 23.000 23.000 0.92 24.963 Jan-17 0 0 0.99 0 Feb-17 0 0 0.92 0 Mar-17 0 0 1.12 0 A. Actual & Normalized Data 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 12. Growth-Adjusted Seasonal Factors Model 12 The next section seasonally-adjusts the data, using one of the 3 sets of seasonal factors. TrendModel: Calc 1 2 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 197 198 199 200 201 202 203 204 205 A B C D E F G H I J K L Calculations Unit: 1 In Use (1 = None; 2 = Initial; 3 = Final) : 2 Actuals Adjust- ments Adjusted Actuals Normalization Factors Normalized Data None Initial Revised In Use Seasonally- Adjusted: Monthly Seasonally- Adjusted: 3- Mo Avg Jan-01 27.844 27.844 1.05 26.510 1.00 1.00 1.03 1.00 26.406 25.412 Feb-01 21.631 21.631 0.92 23.459 1.00 0.96 0.97 0.96 24.418 25.666 Mar-01 27.970 27.970 1.07 26.229 1.00 1.00 1.01 1.00 26.174 25.849 Apr-01 25.529 25.529 0.95 26.799 1.00 0.99 1.01 0.99 26.954 25.517 May-01 24.568 24.568 1.06 23.175 1.00 0.99 1.00 0.99 23.424 24.712 Jun-01 24.674 24.674 1.02 24.284 1.00 1.02 1.02 1.02 23.756 24.153 Jul-01 23.878 23.878 0.96 24.883 1.00 0.98 0.97 0.98 25.279 24.015 Aug-01 23.591 23.591 1.10 21.354 1.00 0.93 0.89 0.93 23.011 27.767 Sep-01 25.417 25.417 0.72 35.098 1.00 1.00 1.01 1.00 35.011 28.406 Oct-01 30.229 30.229 1.09 27.692 1.00 1.02 1.02 1.02 27.195 29.510 Nov-01 26.672 26.672 0.99 27.054 1.00 1.03 1.00 1.03 26.326 27.069 Dec-01 25.506 25.506 0.86 29.529 1.00 1.07 1.07 1.07 27.685 27.651 Jan-02 29.943 29.943 1.03 29.056 1.00 1.00 1.03 1.00 28.941 28.754Feb-02 26.255 26.255 0.92 28.474 1.00 0.96 0.97 0.96 29.637 28.775Mar-02 26.743 26.743 0.96 27.806 1.00 1.00 1.01 1.00 27.747 28.260Apr-02 28.761 28.761 1.06 27.239 1.00 0.99 1.01 0.99 27.397 27.017May-02 27.152 27.152 1.06 25.632 1.00 0.99 1.00 0.99 25.908 28.461Jun-02 31.740 31.740 0.97 32.791 1.00 1.02 1.02 1.02 32.079 33.049Jul-02 41.499 41.499 1.02 40.516 1.00 0.98 0.97 0.98 41.160 34.472Aug-02 29.511 29.511 1.05 28.003 1.00 0.93 0.89 0.93 30.177 33.477Sep-02 28.180 28.180 0.97 29.168 1.00 1.00 1.01 1.00 29.095 31.102Oct-02 38.061 38.061 1.10 34.657 1.00 1.02 1.02 1.02 34.034 31.178Nov-02 29.087 29.087 0.93 31.245 1.00 1.03 1.00 1.03 30.404 30.700Dec-02 26.205 26.205 0.89 29.503 1.00 1.07 1.07 1.07 27.660 29.293 Jul-16 22.328 22.328 0.96 23.217 1.00 0.98 0.97 0.98 23.585 24.695 Aug-16 23.490 23.490 1.11 21.141 1.00 0.93 0.89 0.93 22.782 23.801 Sep-16 25.282 25.282 1.01 25.100 1.00 1.00 1.01 1.00 25.037 23.457 Oct-16 22.795 22.795 0.99 22.964 1.00 1.02 1.02 1.02 22.552 24.850 Nov-16 27.327 27.327 0.99 27.708 1.00 1.03 1.00 1.03 26.963 24.306 Dec-16 23.000 23.000 0.92 24.963 1.00 1.07 1.07 1.07 23.404 25.183 Jan-17 0 0 0.99 0 1.00 1.00 1.03 1.00 Feb-17 0 0 0.92 0 1.00 0.96 0.97 0.96 Mar-17 0 0 1.12 0 1.00 1.00 1.01 1.00 Seasonal Factors A. Actual & Normalized Data B. Seasonally-Adjusted Data 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 13. Growth-Adjusted Seasonal Factors Model 13 The 3rd section estimates the data trend, using the Growth Rates and Events that will be estimated in the “Trend” tab. TrendModel: Calc 1 2 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 197 198 199 200 201 202 203 204 205 A E F G H I J K L M N O P Calculations1 In Use (1 = None; 2 = Initial; 3 = Final) : 2 Start: 25.000 Normalization Factors Normalized Data None Initial "Final" In Use Seasonally- Adjusted: Monthly Seasonally- Adjusted: 3- Mo Avg Growth Rate 1-Time Events Estimated Trend Estimated Trend Values Jan-01 1.05 26.510 1.00 1.00 1.03 1.00 26.406 25.412 2.0% 0.0% 25.042 26.406 Feb-01 0.92 23.459 1.00 0.96 0.97 0.96 24.418 25.666 2.0% 0.0% 25.083 22.221 Mar-01 1.07 26.229 1.00 1.00 1.01 1.00 26.174 25.849 2.0% 0.0% 25.125 26.849 Apr-01 0.95 26.799 1.00 0.99 1.01 0.99 26.954 25.517 2.0% 0.0% 25.167 23.836 May-01 1.06 23.175 1.00 0.99 1.00 0.99 23.424 24.712 2.0% 0.0% 25.209 26.441 Jun-01 1.02 24.284 1.00 1.02 1.02 1.02 23.756 24.153 2.0% 0.0% 25.251 26.226 Jul-01 0.96 24.883 1.00 0.98 0.97 0.98 25.279 24.015 2.0% 0.0% 25.293 23.892 Aug-01 1.10 21.354 1.00 0.93 0.89 0.93 23.011 27.767 2.0% 0.0% 25.335 25.973 Sep-01 0.72 35.098 1.00 1.00 1.01 1.00 35.011 28.406 2.0% 30.0% 32.991 23.950 Oct-01 1.09 27.692 1.00 1.02 1.02 1.02 27.195 29.510 2.0% -20.0% 26.437 29.386 Nov-01 0.99 27.054 1.00 1.03 1.00 1.03 26.326 27.069 2.0% 0.0% 26.481 26.829 Dec-01 0.86 29.529 1.00 1.07 1.07 1.07 27.685 27.651 2.0% 0.0% 26.525 24.437 Jan-02 1.03 29.056 1.00 1.00 1.03 1.00 28.941 28.754 2.0% 0.0% 26.569 27.489Feb-02 0.92 28.474 1.00 0.96 0.97 0.96 29.637 28.775 2.0% 0.0% 26.613 23.576Mar-02 0.96 27.806 1.00 1.00 1.01 1.00 27.747 28.260 2.0% 0.0% 26.658 25.693Apr-02 1.06 27.239 1.00 0.99 1.01 0.99 27.397 27.017 2.0% 0.0% 26.702 28.032May-02 1.06 25.632 1.00 0.99 1.00 0.99 25.908 28.461 2.0% 0.0% 26.747 28.031Jun-02 0.97 32.791 1.00 1.02 1.02 1.02 32.079 33.049 2.0% 0.0% 26.791 26.508Jul-02 1.02 40.516 1.00 0.98 0.97 0.98 41.160 34.472 1.0% 0.0% 26.813 27.034Aug-02 1.05 28.003 1.00 0.93 0.89 0.93 30.177 33.477 1.0% 0.0% 26.836 26.244Sep-02 0.97 29.168 1.00 1.00 1.01 1.00 29.095 31.102 1.0% 0.0% 26.858 26.014Oct-02 1.10 34.657 1.00 1.02 1.02 1.02 34.034 31.178 1.0% 0.0% 26.881 30.061Nov-02 0.93 31.245 1.00 1.03 1.00 1.03 30.404 30.700 1.0% 0.0% 26.903 25.738Dec-02 0.89 29.503 1.00 1.07 1.07 1.07 27.660 29.293 1.0% 0.0% 26.925 25.509 Jul-16 0.96 23.217 1.00 0.98 0.97 0.98 23.585 24.695 1.0% 0.0% 30.841 29.197 Aug-16 1.11 21.141 1.00 0.93 0.89 0.93 22.782 23.801 1.0% 0.0% 30.867 31.826 Sep-16 1.01 25.100 1.00 1.00 1.01 1.00 25.037 23.457 1.0% 0.0% 30.892 31.195 Oct-16 0.99 22.964 1.00 1.02 1.02 1.02 22.552 24.850 0.0% 0.0% 30.892 31.226 Nov-16 0.99 27.708 1.00 1.03 1.00 1.03 26.963 24.306 0.0% 0.0% 30.892 31.310 Dec-16 0.92 24.963 1.00 1.07 1.07 1.07 23.404 25.183 0.0% 0.0% 30.892 30.359 Jan-17 0.99 0 1.00 1.00 1.03 1.00 0.0% 0.0% Feb-17 0.92 0 1.00 0.96 0.97 0.96 0.0% 2.0% Mar-17 1.12 0 1.00 1.00 1.01 1.00 0.0% 0.0% Seasonal Factors A. Actual & Normalized Data B. Seasonally-Adjusted Data C. Estimated Trend 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 14. Growth-Adjusted Seasonal Factors Model 14 The 4th section is the forecast, which takes the estimated trend and extrapolates it using the assumptions for future growth rate & events. TrendModel: Calc 1 2 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 197 198 199 200 201 202 203 204 205 A M N O P Q R Calculations Start: 25.000 Growth Rate 1-Time Events Estimated Trend Estimated Trend Values Extrapolated Trend Extrapolated Trend Values (= Forecast) Jan-01 2.0% 0.0% 25.042 26.406 Feb-01 2.0% 0.0% 25.083 22.221 Mar-01 2.0% 0.0% 25.125 26.849 Apr-01 2.0% 0.0% 25.167 23.836 May-01 2.0% 0.0% 25.209 26.441 Jun-01 2.0% 0.0% 25.251 26.226 Jul-01 2.0% 0.0% 25.293 23.892 Aug-01 2.0% 0.0% 25.335 25.973 Sep-01 2.0% 30.0% 32.991 23.950 Oct-01 2.0% -20.0% 26.437 29.386 Nov-01 2.0% 0.0% 26.481 26.829 Dec-01 2.0% 0.0% 26.525 24.437 Jan-02 2.0% 0.0% 26.569 27.489Feb-02 2.0% 0.0% 26.613 23.576Mar-02 2.0% 0.0% 26.658 25.693Apr-02 2.0% 0.0% 26.702 28.032May-02 2.0% 0.0% 26.747 28.031Jun-02 2.0% 0.0% 26.791 26.508Jul-02 1.0% 0.0% 26.813 27.034Aug-02 1.0% 0.0% 26.836 26.244Sep-02 1.0% 0.0% 26.858 26.014Oct-02 1.0% 0.0% 26.881 30.061Nov-02 1.0% 0.0% 26.903 25.738Dec-02 1.0% 0.0% 26.925 25.509 Jul-16 1.0% 0.0% 30.841 29.197 Aug-16 1.0% 0.0% 30.867 31.826 Sep-16 1.0% 0.0% 30.892 31.195 Oct-16 0.0% 0.0% 30.892 31.226 Nov-16 0.0% 0.0% 30.892 31.310 Dec-16 0.0% 0.0% 30.892 30.359 Jan-17 0.0% 0.0% 30.892 30.614 Feb-17 0.0% 2.0% 31.510 27.874 Mar-17 0.0% 0.0% 31.510 35.249 C. Estimated Trend D. Forecasts 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 15. Growth-Adjusted Seasonal Factors Model 15 The 5th & final section picks up the past & projected trend, as well as the past actuals and extrapolated trend values. TrendModel: Calc 1 2 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 197 198 199 200 201 202 203 204 205 A B O P Q R S T U Calculations 25.000 Actuals Estimated Trend Estimated Trend Values Extrapolated Trend Extrapolated Trend Values (= Forecast) Estimated (& Extrapolated) Trend Actual (& Extrapolated) Values Estimate vs Actual: Diff Jan-01 27.844 25.042 26.406 25.042 27.844 (2.802) Feb-01 21.631 25.083 22.221 25.083 21.631 3.452 Mar-01 27.970 25.125 26.849 25.125 27.970 (2.845) Apr-01 25.529 25.167 23.836 25.167 25.529 (0.362) May-01 24.568 25.209 26.441 25.209 24.568 0.641 Jun-01 24.674 25.251 26.226 25.251 24.674 0.577 Jul-01 23.878 25.293 23.892 25.293 23.878 1.415 Aug-01 23.591 25.335 25.973 25.335 23.591 1.745 Sep-01 25.417 32.991 23.950 32.991 25.417 7.574 Oct-01 30.229 26.437 29.386 26.437 30.229 (3.792) Nov-01 26.672 26.481 26.829 26.481 26.672 (0.191) Dec-01 25.506 26.525 24.437 26.525 25.506 1.019 Jan-02 29.943 26.569 27.489 26.569 29.943 (3.374)Feb-02 26.255 26.613 23.576 26.613 26.255 0.358Mar-02 26.743 26.658 25.693 26.658 26.743 (0.085)Apr-02 28.761 26.702 28.032 26.702 28.761 (2.059)May-02 27.152 26.747 28.031 26.747 27.152 (0.405)Jun-02 31.740 26.791 26.508 26.791 31.740 (4.948)Jul-02 41.499 26.813 27.034 26.813 41.499 (14.685)Aug-02 29.511 26.836 26.244 26.836 29.511 (2.675)Sep-02 28.180 26.858 26.014 26.858 28.180 (1.322)Oct-02 38.061 26.881 30.061 26.881 38.061 (11.180)Nov-02 29.087 26.903 25.738 26.903 29.087 (2.184)Dec-02 26.205 26.925 25.509 26.925 26.205 0.720 Jul-16 22.328 30.841 29.197 30.841 22.328 6.869 Aug-16 23.490 30.867 31.826 30.867 23.490 8.336 Sep-16 25.282 30.892 31.195 30.892 25.282 5.913 Oct-16 22.795 30.892 31.226 30.892 22.795 8.431 Nov-16 27.327 30.892 31.310 30.892 27.327 3.983 Dec-16 23.000 30.892 30.359 30.892 23.000 7.359 Jan-17 0 30.892 30.614 30.892 30.614 0 Feb-17 0 31.510 27.874 31.510 27.874 0 Mar-17 0 31.510 35.249 31.510 35.249 0 E. Estimate & ActualA. Actual & Normalized DataC. Estimated Trend D. Forecasts 1. Introduction 2. Inputs 3. Calc 4. Trend Revise Col. U & its explanation. Change next page and start page showing this as well
  • 16. Growth-Adjusted Seasonal Factors Model 16 The bottom of the “Calc” tab calculates annual totals for all the columns. TrendModel: Calc 1 2 7 8 9 10 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 A B C D E F G H I J K L M N O P Q R S T U Calculations Unit: 1 In Use (1 = None; 2 = Initial; 3 = Final) : 2 Start: 25.000 Actuals Adjust- ments Adjusted Actuals Normalization Factors Normalized Data None Initial "Final" In Use Seasonally- Adjusted: Monthly Seasonally- Adjusted: 3- Mo Avg Growth Rate 1-Time Events Estimated Trend Estimated Trend Values Extrapolated Trend Extrapolated Trend Values (= Forecast) Estimated (& Extrapolated) Trend Actual (& Extrapolated) Values Estimate vs Actual: Diff Annual Totals 2001 308 0 308 0.983 316 1.000 1.000 1.000 1.000 316 316 2.0% 10.0% 314 306 0 0 314 308 6 2002 363 0 363 0.997 364 1.000 1.000 1.000 1.000 364 365 1.5% 0.0% 321 320 0 0 321 363 (42) 2003 352 0 352 1.000 352 1.000 1.000 1.000 1.000 352 353 1.0% 0.0% 325 325 0 0 325 352 (28) 2004 370 0 370 1.003 370 1.000 1.000 1.000 1.000 369 367 1.0% 0.0% 328 329 0 0 328 370 (42) 2005 415 0 415 1.004 414 1.000 1.000 1.000 1.000 414 416 1.0% 0.0% 331 332 0 0 331 415 (84) 2006 458 0 458 0.997 460 1.000 1.000 1.000 1.000 460 459 1.0% 0.0% 335 334 0 0 335 458 (124) 2007 532 0 532 0.999 531 1.000 1.000 1.000 1.000 533 537 1.0% 0.0% 338 338 0 0 338 532 (194) 2008 660 0 660 1.003 656 1.000 1.000 1.000 1.000 656 650 1.0% 0.0% 342 343 0 0 342 660 (319) 2009 549 0 549 0.999 550 1.000 1.000 1.000 1.000 551 551 1.0% 0.0% 345 344 0 0 345 549 (204) 2010 445 0 445 0.999 445 1.000 1.000 1.000 1.000 446 447 1.0% 0.0% 348 348 0 0 348 445 (96) 2011 384 0 384 1.003 381 1.000 1.000 1.000 1.000 382 381 1.0% 0.0% 352 353 0 0 352 384 (32) 2012 287 0 287 0.998 288 1.000 1.000 1.000 1.000 288 288 1.0% 0.0% 355 354 0 0 355 287 69 2013 261 0 261 0.996 262 1.000 1.000 1.000 1.000 262 262 1.0% 0.0% 359 357 0 0 359 261 98 2014 262 0 262 1.000 262 1.000 1.000 1.000 1.000 262 261 1.0% 0.0% 363 362 0 0 363 262 101 2015 299 0 299 0.999 300 1.000 1.000 1.000 1.000 300 301 1.0% 0.0% 366 366 0 0 366 299 67 2016 315 0 315 1.002 315 1.000 1.000 1.000 1.000 315 315 0.8% 0.0% 370 370 0 0 370 315 55 2017 0 0 0 0.997 0 1.000 1.000 1.000 1.000 0 0 0.0% 2.0% 0 0 378 376 378 376 0 2018 0 0 0 0.999 0 1.000 1.000 1.000 1.000 0 0 0.0% 0.0% 0 0 378 377 378 377 0 2019 0 0 0 0.996 0 1.000 1.000 1.000 1.000 0 0 0.0% 0.0% 0 0 378 376 378 376 0 2020 0 0 0 1.004 0 1.000 1.000 1.000 1.000 0 0 0.0% 0.0% 0 0 378 379 378 379 0 E. Estimate & Actual Seasonal Factors A. Actual & Normalized Data B. Seasonally-Adjusted Data C. Estimated Trend D. Forecasts 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 17. Growth-Adjusted Seasonal Factors Model 17 The “Trend” tab is divided into three sections. TrendModel: Trend 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 49 50 51 52 53 54 55 56 57 58 59 60 61 62 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 A C D E F G H I J K L M N O P Q R S X Y Z AA AB AC AD AE AF AG AH AI AJ Estimating Trend Seasonal Factors In Use: Initial 2 (1 = None; 2 = Initial; 3 = Final) Growth Rate 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Feb 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Mar 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Apr 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% May 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Jun 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Jul 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Aug 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Sep 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Oct 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0% Nov 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0% Dec 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0% Start 25.0 Events 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan Feb 2.0% Mar Apr May Jun Jul Aug Sep 30.0% Oct -20.0% Nov Dec Actuals vs Estimate by Year 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Actual 307.5 363.1 352.4 369.6 415.1 458.5 532.0 660.3 549.3 444.7 383.9 286.8 260.7 261.9 299.1 315.5 0.0 Est 306.4 319.9 324.8 329.0 332.4 333.5 337.5 342.5 344.5 348.1 352.7 354.4 357.3 362.4 365.8 370.4 376.1 Diff -1.1 -43.2 -27.6 -40.6 -82.7 -125.0 -194.5 -317.8 -204.8 -96.6 -31.2 67.6 96.7 100.5 66.7 54.9 % Diff -0.3% -11.9% -7.8% -11.0% -19.9% -27.3% -36.6% -48.1% -37.3% -21.7% -8.1% 23.6% 37.1% 38.4% 22.3% 17.4% Total 2001-16 YTD Actual 6,260 315.5 Est 5,482 370.4 Diff (779) 54.9 % Diff -12.4% 17.4% Seasonal Factors Normalized Data 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 26.5 29.1 29.9 34.2 33.2 39.6 38.3 58.1 46.4 35.6 33.2 24.7 22.0 20.7 24.5 31.2 0.0 Feb 23.5 28.5 27.5 30.6 33.0 37.5 40.0 47.0 54.6 35.5 31.8 24.4 22.2 22.1 23.2 30.9 0.0 Mar 26.2 27.8 29.9 30.7 35.6 35.9 43.9 55.7 61.8 33.2 31.9 24.8 22.4 22.1 24.1 28.4 0.0 Apr 26.8 27.2 29.6 31.9 35.8 37.2 40.2 43.9 53.5 41.0 27.8 24.6 22.2 21.8 22.6 25.7 0.0 May 23.2 25.6 31.0 31.5 32.2 41.5 41.3 42.5 52.6 54.4 28.5 26.4 21.9 19.4 21.8 25.6 0.0 Jun 24.3 32.8 31.5 27.1 32.1 41.4 45.0 50.5 43.7 43.5 30.0 26.4 26.0 21.1 24.6 28.3 0.0 Jul 24.9 40.5 30.2 29.3 31.5 38.7 49.0 60.5 38.4 36.5 27.3 24.5 20.5 19.2 23.0 23.2 0.0 Aug 21.4 28.0 25.1 25.9 30.6 33.3 55.4 44.6 41.2 32.0 43.6 20.2 19.1 17.8 27.5 21.1 0.0 Sep 35.1 29.2 29.7 27.7 36.1 37.3 40.3 70.1 42.8 32.2 35.0 23.9 21.8 21.4 27.8 25.1 0.0 Oct 27.7 34.7 30.0 32.9 40.7 39.1 41.6 75.7 41.4 33.9 34.5 20.2 20.8 26.7 26.4 23.0 0.0 Nov 27.1 31.2 27.8 32.4 36.4 40.4 52.2 57.3 35.2 33.9 29.6 23.1 20.3 22.4 25.2 27.7 0.0 Dec 29.5 29.5 29.6 35.2 36.8 38.2 44.1 50.2 38.1 33.7 27.6 24.7 23.0 27.6 28.9 25.0 0.0 Growth Rate (Monthly Basis) 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Feb 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 2.0% Mar 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Apr 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% May 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Jun 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Jul 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Aug 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Sep 30.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Oct -19.9% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0% Nov 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0% Dec 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0% Cumulative Growth Rate 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Feb 0.3% 0.3% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 2.0% Mar 0.5% 0.5% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 2.0% Apr 0.7% 0.7% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 2.0% May 0.8% 0.8% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 2.0% Jun 1.0% 1.0% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 2.0% Jul 1.2% 1.1% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 2.0% Aug 1.3% 1.2% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 2.0% Sep 32.0% 1.3% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 2.0% Oct 5.7% 1.3% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 2.0% Nov 5.9% 1.4% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.8% 2.0% Dec 6.1% 1.5% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.8% 2.0% Avg 4.6% 0.9% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 1.8% Indexed Cumulative Growth 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 0.96 0.99 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.98 Feb 0.96 0.99 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Mar 0.96 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Apr 0.96 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 May 0.96 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Jun 0.97 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Jul 0.97 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Aug 0.97 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Sep 1.26 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Oct 1.01 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Nov 1.01 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Dec 1.01 1.01 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Avg 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Growth-Adjusted Normalized Data 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 27.7 29.3 30.1 34.3 33.3 39.8 38.5 58.3 46.7 35.8 33.3 24.8 22.1 20.8 24.6 31.3 0.0 Feb 24.5 28.6 27.6 30.7 33.1 37.6 40.1 47.2 54.8 35.6 31.9 24.5 22.3 22.2 23.3 31.0 0.0 Mar 27.3 27.9 30.0 30.8 35.7 36.0 44.0 55.9 61.9 33.3 32.0 24.9 22.4 22.1 24.2 28.4 0.0 Apr 27.9 27.3 29.7 32.0 35.9 37.2 40.3 44.0 53.6 41.1 27.9 24.6 22.2 21.8 22.6 25.8 0.0 May 24.1 25.7 31.0 31.5 32.2 41.5 41.4 42.6 52.6 54.5 28.6 26.4 21.9 19.4 21.9 25.6 0.0 Jun 25.2 32.8 31.5 27.2 32.1 41.5 45.1 50.6 43.7 43.6 30.0 26.4 26.0 21.1 24.6 28.3 0.0 Jul 25.7 40.5 30.2 29.3 31.5 38.6 49.0 60.4 38.4 36.5 27.2 24.5 20.5 19.2 23.0 23.2 0.0 Aug 22.1 27.9 25.1 25.9 30.6 33.2 55.4 44.6 41.1 32.0 43.6 20.2 19.0 17.8 27.4 21.1 0.0 Sep 27.8 29.1 29.7 27.6 36.0 37.2 40.2 70.0 42.7 32.1 34.9 23.9 21.7 21.3 27.8 25.0 0.0 Oct 27.4 34.5 29.9 32.8 40.6 39.0 41.5 75.5 41.2 33.8 34.4 20.2 20.7 26.6 26.4 22.9 0.0 Nov 26.7 31.1 27.7 32.3 36.3 40.3 52.0 57.1 35.0 33.7 29.5 23.0 20.3 22.3 25.1 27.6 0.0 Dec 29.1 29.3 29.5 35.0 36.7 38.0 43.9 50.0 37.9 33.6 27.5 24.6 22.9 27.5 28.7 24.9 0.0 Avg 26.3 30.3 29.3 30.8 34.5 38.3 44.3 54.7 45.8 37.1 31.7 24.0 21.8 21.8 25.0 26.3 0.0 0.2% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% Growth-Adjusted Normalized Data: Factored Max Permitted Standard Deviations: 2.0 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Avg Std Dev Low High Wtd Avg Jan 1.05 0.97 1.03 1.11 0.97 1.04 0.87 1.07 1.02 0.96 1.05 1.03 1.01 0.95 0.98 1.19 1.02 0.07 0.87 1.17 1.03 Feb 0.93 0.94 0.94 1.00 0.96 0.98 0.91 0.86 1.20 0.96 1.01 1.02 1.02 1.02 0.93 1.18 0.99 0.09 0.81 1.17 0.97 Mar 1.04 0.92 1.02 1.00 1.03 0.94 0.99 1.02 1.35 0.90 1.01 1.04 1.03 1.01 0.97 1.08 1.02 0.10 0.82 1.22 1.01 Apr 1.06 0.90 1.01 1.04 1.04 0.97 0.91 0.81 1.17 1.11 0.88 1.03 1.02 1.00 0.91 0.98 0.99 0.09 0.80 1.17 1.01 May 0.91 0.85 1.06 1.02 0.93 1.08 0.93 0.78 1.15 1.47 0.90 1.10 1.00 0.89 0.88 0.98 1.00 0.16 0.67 1.32 1.00 Jun 0.96 1.08 1.07 0.88 0.93 1.08 1.02 0.92 0.95 1.17 0.95 1.10 1.19 0.97 0.99 1.08 1.02 0.09 0.84 1.20 1.02 Jul 0.98 1.33 1.03 0.95 0.91 1.01 1.11 1.11 0.84 0.98 0.86 1.02 0.94 0.88 0.92 0.88 0.98 0.12 0.74 1.23 0.97 Aug 0.84 0.92 0.86 0.84 0.89 0.87 1.25 0.82 0.90 0.86 1.37 0.84 0.87 0.81 1.10 0.80 0.93 0.17 0.59 1.26 0.89 Sep 1.06 0.96 1.01 0.90 1.04 0.97 0.91 1.28 0.93 0.87 1.10 0.99 0.99 0.98 1.11 0.95 1.00 0.10 0.80 1.21 1.01 Oct 1.04 1.14 1.02 1.07 1.18 1.02 0.94 1.38 0.90 0.91 1.08 0.84 0.95 1.22 1.06 0.87 1.04 0.14 0.75 1.32 1.02 Nov 1.02 1.03 0.95 1.05 1.05 1.05 1.17 1.04 0.76 0.91 0.93 0.96 0.93 1.02 1.01 1.05 1.00 0.09 0.81 1.18 1.00 Dec 1.11 0.97 1.00 1.14 1.06 0.99 0.99 0.91 0.83 0.90 0.87 1.02 1.05 1.26 1.15 0.95 1.01 0.11 0.79 1.24 1.07 Avg 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.11 0.78 1.22 1.00 Data Accepted? 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Total Jan 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 Feb 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 Mar 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 Apr 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 May 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 Jun 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Jul 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Aug 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 Sep 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 Oct 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 Nov 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 Dec 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 OK? 1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 8 Use Std Dev? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Seasonal Factor Weights 1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 0 8 Accepted Range 022.0 24.0 26.0 28.0 30.0 32.0 34.0 36.0 38.0 40.0 Jan-01 Jan-02 Jan-03 Jan-04 Sales Volumes (Billions) NYSE Monthly Sales Volumes Seasonally-Adjusted Actual (& Extrapolated) Values Seasonally-Adjusted: Monthly Seasonally-Adjusted: 3-Mo Avg 0.70 0.80 0.90 1.00 1.10 1.20 1.30 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Seasonal Factors Final Initial Low High Trend Estimates Seasonal Factors Calculation Chart 1. Introduction 2. Inputs 3. Calc 4. Trend Model Structure: Trend
  • 18. Growth-Adjusted Seasonal Factors Model 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 49 50 51 52 53 54 55 56 57 58 59 60 61 62 A C D E F G H I J K L M N O P Q R S X Estimating Trend Growth Rate 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Feb 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Mar 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Apr 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% May 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Jun 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Jul 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Aug 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Sep 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Oct 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0% Nov 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0% Dec 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0% Start 25.0 Events 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan Feb 2.0% Mar Apr May Jun Jul 10.0% Aug Sep 30.0% Oct -20.0% Nov Dec Actuals vs Estimate by Year 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Actual 307.5 363.1 352.4 369.6 415.1 458.5 532.0 660.3 549.3 444.7 383.9 286.8 260.7 261.9 299.1 315.5 0.0 Est 306.4 336.0 357.3 361.9 365.6 366.9 371.3 376.8 378.9 382.9 387.9 389.9 393.1 398.7 402.4 407.4 413.8 Diff -1.1 -27.1 4.9 -7.7 -49.4 -91.6 -160.8 -283.5 -170.4 -61.8 4.1 103.1 132.4 136.8 103.3 91.9 % Diff -0.3% -7.5% 1.4% -2.1% -11.9% -20.0% -30.2% -42.9% -31.0% -13.9% 1.1% 35.9% 50.8% 52.2% 34.5% 29.1% Total 2001-16 YTD Actual 6,260 315.5 Est 5,983 407.4 Diff (277) 91.9 % Diff -4.4% 29.1% 22.0 24.0 26.0 28.0 30.0 32.0 34.0 36.0 38.0 40.0 18 The “Estimating Trend” section is the steering wheel for the model; it’s where you insert your monthly estimates of the growth rate and events. TrendModel: Trend Growth Rates Events Starting Point Actuals vs Estimate Model Structure: Trend Estimates 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 19. Growth-Adjusted Seasonal Factors Model 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 49 50 51 52 53 54 55 56 57 58 59 60 61 62 A C D E F Estimating Trend Growth Rate 2001 2002 2003 2004 Jan 2.0% 2.0% 1.0% 1.0% Feb 2.0% 2.0% 1.0% 1.0% Mar 2.0% 2.0% 1.0% 1.0% Apr 2.0% 2.0% 1.0% 1.0% May 2.0% 2.0% 1.0% 1.0% Jun 2.0% 2.0% 1.0% 1.0% Jul 2.0% 1.0% 1.0% 1.0% Aug 2.0% 1.0% 1.0% 1.0% Sep 2.0% 1.0% 1.0% 1.0% Oct 2.0% 1.0% 1.0% 1.0% Nov 2.0% 1.0% 1.0% 1.0% Dec 2.0% 1.0% 1.0% 1.0% Start 25.0 Events 2001 2002 2003 2004 Jan Feb Mar Apr May Jun Jul 10.0% Aug Sep 30.0% Oct -20.0% Nov Dec Actuals vs Estimate by Year 2001 2002 2003 2004 Actual 307.5 363.1 352.4 369.6 Est 306.4 336.0 357.3 361.9 Diff -1.1 -27.1 4.9 -7.7 % Diff -0.3% -7.5% 1.4% -2.1% 19 The Growth Rates are the estimates of the annual rate at which the data is growing; conditional formatting highlights changes in the rate. TrendModel: Trend Growth Rates 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 20. Growth-Adjusted Seasonal Factors Model 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 49 50 51 52 53 54 55 56 57 58 59 60 61 62 A C D E F Estimating Trend Growth Rate 2001 2002 2003 2004 Jan 2.0% 2.0% 1.0% 1.0% Feb 2.0% 2.0% 1.0% 1.0% Mar 2.0% 2.0% 1.0% 1.0% Apr 2.0% 2.0% 1.0% 1.0% May 2.0% 2.0% 1.0% 1.0% Jun 2.0% 2.0% 1.0% 1.0% Jul 2.0% 1.0% 1.0% 1.0% Aug 2.0% 1.0% 1.0% 1.0% Sep 2.0% 1.0% 1.0% 1.0% Oct 2.0% 1.0% 1.0% 1.0% Nov 2.0% 1.0% 1.0% 1.0% Dec 2.0% 1.0% 1.0% 1.0% Start 25.0 Events 2001 2002 2003 2004 Jan Feb Mar Apr May Jun Jul 10.0% Aug Sep 30.0% Oct -20.0% Nov Dec Actuals vs Estimate by Year 2001 2002 2003 2004 Actual 307.5 363.1 352.4 369.6 Est 306.4 336.0 357.3 361.9 Diff -1.1 -27.1 4.9 -7.7 % Diff -0.3% -7.5% 1.4% -2.1% 20 The Starting Point is the approximate level at the outset of the period being modeled. TrendModel: Trend Starting Point 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 21. Growth-Adjusted Seasonal Factors Model 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 49 50 51 52 53 54 55 56 57 58 59 60 61 62 A C D E F Estimating Trend Growth Rate 2001 2002 2003 2004 Jan 2.0% 2.0% 1.0% 1.0% Feb 2.0% 2.0% 1.0% 1.0% Mar 2.0% 2.0% 1.0% 1.0% Apr 2.0% 2.0% 1.0% 1.0% May 2.0% 2.0% 1.0% 1.0% Jun 2.0% 2.0% 1.0% 1.0% Jul 2.0% 1.0% 1.0% 1.0% Aug 2.0% 1.0% 1.0% 1.0% Sep 2.0% 1.0% 1.0% 1.0% Oct 2.0% 1.0% 1.0% 1.0% Nov 2.0% 1.0% 1.0% 1.0% Dec 2.0% 1.0% 1.0% 1.0% Start 25.0 Events 2001 2002 2003 2004 Jan Feb Mar Apr May Jun Jul 10.0% Aug Sep 30.0% Oct -20.0% Nov Dec Actuals vs Estimate by Year 2001 2002 2003 2004 Actual 307.5 363.1 352.4 369.6 Est 306.4 336.0 357.3 361.9 Diff -1.1 -27.1 4.9 -7.7 % Diff -0.3% -7.5% 1.4% -2.1% 21 Events are the estimates of when a step function takes place, when there is a sudden shift in the level of the data. Most months do not have events. TrendModel: Trend Events 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 22. Growth-Adjusted Seasonal Factors Model 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 49 50 51 52 53 54 55 56 57 58 59 60 61 62 A C D E F Estimating Trend Growth Rate 2001 2002 2003 2004 Jan 2.0% 2.0% 1.0% 1.0% Feb 2.0% 2.0% 1.0% 1.0% Mar 2.0% 2.0% 1.0% 1.0% Apr 2.0% 2.0% 1.0% 1.0% May 2.0% 2.0% 1.0% 1.0% Jun 2.0% 2.0% 1.0% 1.0% Jul 2.0% 1.0% 1.0% 1.0% Aug 2.0% 1.0% 1.0% 1.0% Sep 2.0% 1.0% 1.0% 1.0% Oct 2.0% 1.0% 1.0% 1.0% Nov 2.0% 1.0% 1.0% 1.0% Dec 2.0% 1.0% 1.0% 1.0% Start 25.0 Events 2001 2002 2003 2004 Jan Feb Mar Apr May Jun Jul 10.0% Aug Sep 30.0% Oct -20.0% Nov Dec Actuals vs Estimate by Year 2001 2002 2003 2004 Actual 307.5 363.1 352.4 369.6 Est 306.4 336.0 357.3 361.9 Diff -1.1 -27.1 4.9 -7.7 % Diff -0.3% -7.5% 1.4% -2.1% 22 The Actual vs Estimate section compares each year’s totals and calculates the difference between the estimated trend and actuals. TrendModel: Trend Actuals vs Estimate 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 23. Growth-Adjusted Seasonal Factors Model 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 49 50 51 52 53 54 55 56 57 58 59 60 61 62 A C D E F G H I J K L M N O P Q R S X Estimating Trend Growth Rate 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Feb 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Mar 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Apr 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% May 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Jun 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Jul 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Aug 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Sep 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Oct 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0% Nov 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0% Dec 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0% Start 25.0 Events 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan Feb 2.0% Mar Apr May Jun Jul 10.0% Aug Sep 30.0% Oct -20.0% Nov Dec Actuals vs Estimate by Year 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Actual 307.5 363.1 352.4 369.6 415.1 458.5 532.0 660.3 549.3 444.7 383.9 286.8 260.7 261.9 299.1 315.5 0.0 Est 306.4 336.0 357.3 361.9 365.6 366.9 371.3 376.8 378.9 382.9 387.9 389.9 393.1 398.7 402.4 407.4 413.8 Diff -1.1 -27.1 4.9 -7.7 -49.4 -91.6 -160.8 -283.5 -170.4 -61.8 4.1 103.1 132.4 136.8 103.3 91.9 % Diff -0.3% -7.5% 1.4% -2.1% -11.9% -20.0% -30.2% -42.9% -31.0% -13.9% 1.1% 35.9% 50.8% 52.2% 34.5% 29.1% Total 2001-16 YTD Actual 6,260 315.5 Est 5,983 407.4 Diff (277) 91.9 % Diff -4.4% 29.1% 22.0 24.0 26.0 28.0 30.0 32.0 34.0 36.0 38.0 40.0 23 The Total Actual vs Estimate table shows how actuals and estimates compare over the entire modeled time period; it also compares current year-to-date. TrendModel: Trend Actuals vs Estimate 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 24. Growth-Adjusted Seasonal Factors Model 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 49 50 51 52 53 54 55 56 57 58 59 60 61 62 69 70 71 72 73 74 75 76 77 78 79 80 81 82 A C D E F G H I J K L M N O P Q R S Estimating Trend Growth Rate 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Feb 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Mar 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Apr 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% May 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Jun 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Jul 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Aug 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Sep 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Oct 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0% Nov 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0% Dec 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0% Start 25.0 Events 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan Feb 2.0% Mar Apr May Jun Jul 10.0% Aug Sep 30.0% Oct -20.0% Nov Dec Actuals vs Estimate by Year 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Actual 307.5 363.1 352.4 369.6 415.1 458.5 532.0 660.3 549.3 444.7 383.9 286.8 260.7 261.9 299.1 315.5 0.0 Est 306.4 336.0 357.3 361.9 365.6 366.9 371.3 376.8 378.9 382.9 387.9 389.9 393.1 398.7 402.4 407.4 413.8 Diff -1.1 -27.1 4.9 -7.7 -49.4 -91.6 -160.8 -283.5 -170.4 -61.8 4.1 103.1 132.4 136.8 103.3 91.9 % Diff -0.3% -7.5% 1.4% -2.1% -11.9% -20.0% -30.2% -42.9% -31.0% -13.9% 1.1% 35.9% 50.8% 52.2% 34.5% 29.1% Total 2001-16 YTD Actual 6,260 315.5 Est 5,983 407.4 Diff (277) 91.9 % Diff -4.4% 29.1% Other Info (e.g. Price Changes) 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 24 While hidden here because it isn’t applicable, there is a section here for “Other Info” that may provide a useful reference. TrendModel: Trend Other Info 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 25. Growth-Adjusted Seasonal Factors Model 25 The Seasonal Factors Calculation section takes the Normalized data, and adjusts for growth & events. TrendModel: Trend 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 A C D E F G H I J K L M N O P Q R S X Y Z AA AB AC AD AE AF AG AH AI Seasonal Factors Normalized Data 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 26.5 29.1 29.9 34.2 33.2 39.6 38.3 58.1 46.4 35.6 33.2 24.7 22.0 20.7 24.5 31.2 0.0 Feb 23.5 28.5 27.5 30.6 33.0 37.5 40.0 47.0 54.6 35.5 31.8 24.4 22.2 22.1 23.2 30.9 0.0 Mar 26.2 27.8 29.9 30.7 35.6 35.9 43.9 55.7 61.8 33.2 31.9 24.8 22.4 22.1 24.1 28.4 0.0 Apr 26.8 27.2 29.6 31.9 35.8 37.2 40.2 43.9 53.5 41.0 27.8 24.6 22.2 21.8 22.6 25.7 0.0 May 23.2 25.6 31.0 31.5 32.2 41.5 41.3 42.5 52.6 54.4 28.5 26.4 21.9 19.4 21.8 25.6 0.0 Jun 24.3 32.8 31.5 27.1 32.1 41.4 45.0 50.5 43.7 43.5 30.0 26.4 26.0 21.1 24.6 28.3 0.0 Jul 24.9 40.5 30.2 29.3 31.5 38.7 49.0 60.5 38.4 36.5 27.3 24.5 20.5 19.2 23.0 23.2 0.0 Aug 21.4 28.0 25.1 25.9 30.6 33.3 55.4 44.6 41.2 32.0 43.6 20.2 19.1 17.8 27.5 21.1 0.0 Sep 35.1 29.2 29.7 27.7 36.1 37.3 40.3 70.1 42.8 32.2 35.0 23.9 21.8 21.4 27.8 25.1 0.0 Oct 27.7 34.7 30.0 32.9 40.7 39.1 41.6 75.7 41.4 33.9 34.5 20.2 20.8 26.7 26.4 23.0 0.0 Nov 27.1 31.2 27.8 32.4 36.4 40.4 52.2 57.3 35.2 33.9 29.6 23.1 20.3 22.4 25.2 27.7 0.0 Dec 29.5 29.5 29.6 35.2 36.8 38.2 44.1 50.2 38.1 33.7 27.6 24.7 23.0 27.6 28.9 25.0 0.0 Growth Rate (Monthly Basis) 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Feb 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 2.0% Mar 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Apr 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% May 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Jun 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Jul 0.2% 10.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Aug 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Sep 30.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Oct -19.9% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0% Nov 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0% Dec 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0% Cumulative Growth Rate 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Feb 0.3% 0.3% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 2.0% Mar 0.5% 0.5% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 2.0% Apr 0.7% 0.7% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 2.0% May 0.8% 0.8% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 2.0% Jun 1.0% 1.0% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 2.0% Jul 1.2% 11.2% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 2.0% Aug 1.3% 11.3% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 2.0% Sep 32.0% 11.4% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 2.0% Oct 5.7% 11.5% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 2.0% Nov 5.9% 11.6% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.8% 2.0% Dec 6.1% 11.7% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.8% 2.0% Avg 4.6% 6.0% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 1.8% Indexed Cumulative Growth 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 0.96 0.94 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.98 Feb 0.96 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Mar 0.96 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Apr 0.96 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 May 0.96 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Jun 0.97 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Jul 0.97 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Aug 0.97 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Sep 1.26 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Oct 1.01 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Nov 1.01 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Dec 1.01 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Avg 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Growth-Adjusted Normalized Data 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 27.7 30.7 30.1 34.3 33.3 39.8 38.5 58.3 46.7 35.8 33.3 24.8 22.1 20.8 24.6 31.3 0.0 Feb 24.5 30.1 27.6 30.7 33.1 37.6 40.1 47.2 54.8 35.6 31.9 24.5 22.3 22.2 23.3 31.0 0.0 Mar 27.3 29.3 30.0 30.8 35.7 36.0 44.0 55.9 61.9 33.3 32.0 24.9 22.4 22.1 24.2 28.4 0.0 Apr 27.9 28.7 29.7 32.0 35.9 37.2 40.3 44.0 53.6 41.1 27.9 24.6 22.2 21.8 22.6 25.8 0.0 May 24.1 26.9 31.0 31.5 32.2 41.5 41.4 42.6 52.6 54.5 28.6 26.4 21.9 19.4 21.9 25.6 0.0 Jun 25.2 34.4 31.5 27.2 32.1 41.5 45.1 50.6 43.7 43.6 30.0 26.4 26.0 21.1 24.6 28.3 0.0 Jul 25.7 38.6 30.2 29.3 31.5 38.6 49.0 60.4 38.4 36.5 27.2 24.5 20.5 19.2 23.0 23.2 0.0 Aug 22.1 26.7 25.1 25.9 30.6 33.2 55.4 44.6 41.1 32.0 43.6 20.2 19.0 17.8 27.4 21.1 0.0 Sep 27.8 27.8 29.7 27.6 36.0 37.2 40.2 70.0 42.7 32.1 34.9 23.9 21.7 21.3 27.8 25.0 0.0 Oct 27.4 33.0 29.9 32.8 40.6 39.0 41.5 75.5 41.2 33.8 34.4 20.2 20.7 26.6 26.4 22.9 0.0 Nov 26.7 29.7 27.7 32.3 36.3 40.3 52.0 57.1 35.0 33.7 29.5 23.0 20.3 22.3 25.1 27.6 0.0 Dec 29.1 28.0 29.5 35.0 36.7 38.0 43.9 50.0 37.9 33.6 27.5 24.6 22.9 27.5 28.7 24.9 0.0 Avg 26.3 30.3 29.3 30.8 34.5 38.3 44.3 54.7 45.8 37.1 31.7 24.0 21.8 21.8 25.0 26.3 0.0 0.2% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% Growth-Adjusted Normalized Data: Factored Max Permitted Standard Deviations: 2.0 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Avg Std Dev Low High Wtd Avg Jan 1.05 1.01 1.03 1.11 0.97 1.04 0.87 1.07 1.02 0.96 1.05 1.03 1.01 0.95 0.98 1.19 1.02 0.07 0.88 1.17 1.03 Feb 0.93 0.99 0.94 1.00 0.96 0.98 0.91 0.86 1.20 0.96 1.01 1.02 1.02 1.02 0.93 1.18 0.99 0.09 0.82 1.17 0.97 Mar 1.04 0.97 1.02 1.00 1.03 0.94 0.99 1.02 1.35 0.90 1.01 1.04 1.03 1.01 0.97 1.08 1.03 0.10 0.83 1.22 1.01 Apr 1.06 0.95 1.01 1.04 1.04 0.97 0.91 0.81 1.17 1.11 0.88 1.03 1.02 1.00 0.91 0.98 0.99 0.09 0.81 1.17 1.01 May 0.91 0.89 1.06 1.02 0.93 1.08 0.93 0.78 1.15 1.47 0.90 1.10 1.00 0.89 0.88 0.98 1.00 0.16 0.68 1.32 1.00 Jun 0.96 1.13 1.07 0.88 0.93 1.08 1.02 0.92 0.95 1.17 0.95 1.10 1.19 0.97 0.99 1.08 1.02 0.10 0.83 1.21 1.02 Jul 0.98 1.27 1.03 0.95 0.91 1.01 1.11 1.11 0.84 0.98 0.86 1.02 0.94 0.88 0.92 0.88 0.98 0.11 0.76 1.20 0.97 Aug 0.84 0.88 0.86 0.84 0.89 0.87 1.25 0.82 0.90 0.86 1.37 0.84 0.87 0.81 1.10 0.80 0.92 0.17 0.59 1.26 0.89 Sep 1.06 0.92 1.01 0.90 1.04 0.97 0.91 1.28 0.93 0.87 1.10 0.99 0.99 0.98 1.11 0.95 1.00 0.10 0.80 1.21 1.01 Oct 1.04 1.09 1.02 1.07 1.18 1.02 0.94 1.38 0.90 0.91 1.08 0.84 0.95 1.22 1.06 0.87 1.03 0.14 0.75 1.32 1.02 Nov 1.02 0.98 0.95 1.05 1.05 1.05 1.17 1.04 0.76 0.91 0.93 0.96 0.93 1.02 1.01 1.05 0.99 0.09 0.81 1.17 1.00 Dec 1.11 0.92 1.00 1.14 1.06 0.99 0.99 0.91 0.83 0.90 0.87 1.02 1.05 1.26 1.15 0.95 1.01 0.12 0.78 1.24 1.07 Avg 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.11 0.78 1.22 1.00 Data Accepted? 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Total Jan 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 Feb 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 Mar 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 Apr 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 May 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 Jun 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Jul 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Aug 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 Sep 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 Oct 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 Nov 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 Dec 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 OK? 1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 8 Use Std Dev? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Seasonal Factor Weights 1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 0 8 Accepted Range 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Seasonal Factors Final Initial Low High 1. Introduction 2. Inputs 3. Calc 4. Trend Model Structure: Seasonal Factors Calculation
  • 26. Growth-Adjusted Seasonal Factors Model 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 A C D E F G H I J K L M N O P Q R S X Seasonal Factors Normalized Data 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 26.5 29.1 29.9 34.2 33.2 39.6 38.3 58.1 46.4 35.6 33.2 24.7 22.0 20.7 24.5 31.2 0.0 Feb 23.5 28.5 27.5 30.6 33.0 37.5 40.0 47.0 54.6 35.5 31.8 24.4 22.2 22.1 23.2 30.9 0.0 Mar 26.2 27.8 29.9 30.7 35.6 35.9 43.9 55.7 61.8 33.2 31.9 24.8 22.4 22.1 24.1 28.4 0.0 Apr 26.8 27.2 29.6 31.9 35.8 37.2 40.2 43.9 53.5 41.0 27.8 24.6 22.2 21.8 22.6 25.7 0.0 May 23.2 25.6 31.0 31.5 32.2 41.5 41.3 42.5 52.6 54.4 28.5 26.4 21.9 19.4 21.8 25.6 0.0 Jun 24.3 32.8 31.5 27.1 32.1 41.4 45.0 50.5 43.7 43.5 30.0 26.4 26.0 21.1 24.6 28.3 0.0 Jul 24.9 40.5 30.2 29.3 31.5 38.7 49.0 60.5 38.4 36.5 27.3 24.5 20.5 19.2 23.0 23.2 0.0 Aug 21.4 28.0 25.1 25.9 30.6 33.3 55.4 44.6 41.2 32.0 43.6 20.2 19.1 17.8 27.5 21.1 0.0 Sep 35.1 29.2 29.7 27.7 36.1 37.3 40.3 70.1 42.8 32.2 35.0 23.9 21.8 21.4 27.8 25.1 0.0 Oct 27.7 34.7 30.0 32.9 40.7 39.1 41.6 75.7 41.4 33.9 34.5 20.2 20.8 26.7 26.4 23.0 0.0 Nov 27.1 31.2 27.8 32.4 36.4 40.4 52.2 57.3 35.2 33.9 29.6 23.1 20.3 22.4 25.2 27.7 0.0 Dec 29.5 29.5 29.6 35.2 36.8 38.2 44.1 50.2 38.1 33.7 27.6 24.7 23.0 27.6 28.9 25.0 0.0 26 We start the seasonal factor calculation procedure by bringing in the normalized data. TrendModel: Trend 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 27. Growth-Adjusted Seasonal Factors Model 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 A C D E F G H I J K L M N O P Q R S X Growth Rate (Monthly Basis) 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Feb 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 2.0% Mar 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Apr 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% May 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Jun 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Jul 0.2% 10.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Aug 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Sep 30.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Oct -19.9% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0% Nov 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0% Dec 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% 0.0% 27 To adjust the data for growth, we bring in the estimates for both the growth rate & events. TrendModel: Trend 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 28. Growth-Adjusted Seasonal Factors Model 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 A C D E F G H I J K L M N O P Q R S X Cumulative Growth Rate 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 0.2% 0.2% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 0.0% Feb 0.3% 0.3% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 2.0% Mar 0.5% 0.5% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 2.0% Apr 0.7% 0.7% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 0.3% 2.0% May 0.8% 0.8% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 0.4% 2.0% Jun 1.0% 1.0% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 2.0% Jul 1.2% 11.2% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 0.6% 2.0% Aug 1.3% 11.3% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 0.7% 2.0% Sep 32.0% 11.4% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 2.0% Oct 5.7% 11.5% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 2.0% Nov 5.9% 11.6% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.9% 0.8% 2.0% Dec 6.1% 11.7% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.8% 2.0% Avg 4.6% 6.0% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 1.8% 28 Next, the growth is accumulated over the year. TrendModel: Trend 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 29. Growth-Adjusted Seasonal Factors Model 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 A C D E F G H I J K L M N O P Q R S X Indexed Cumulative Growth 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 0.96 0.94 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.98 Feb 0.96 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Mar 0.96 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Apr 0.96 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 May 0.96 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Jun 0.97 0.95 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Jul 0.97 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Aug 0.97 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Sep 1.26 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Oct 1.01 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Nov 1.01 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Dec 1.01 1.05 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Avg 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 29 The cumulative growth rates are then indexed, giving us the factors we need to adjust the data for growth and events. TrendModel: Trend 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 30. Growth-Adjusted Seasonal Factors Model 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 A C D E F G H I J K L M N O P Q R S X Growth-Adjusted Normalized Data 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 27.7 30.7 30.1 34.3 33.3 39.8 38.5 58.3 46.7 35.8 33.3 24.8 22.1 20.8 24.6 31.3 0.0 Feb 24.5 30.1 27.6 30.7 33.1 37.6 40.1 47.2 54.8 35.6 31.9 24.5 22.3 22.2 23.3 31.0 0.0 Mar 27.3 29.3 30.0 30.8 35.7 36.0 44.0 55.9 61.9 33.3 32.0 24.9 22.4 22.1 24.2 28.4 0.0 Apr 27.9 28.7 29.7 32.0 35.9 37.2 40.3 44.0 53.6 41.1 27.9 24.6 22.2 21.8 22.6 25.8 0.0 May 24.1 26.9 31.0 31.5 32.2 41.5 41.4 42.6 52.6 54.5 28.6 26.4 21.9 19.4 21.9 25.6 0.0 Jun 25.2 34.4 31.5 27.2 32.1 41.5 45.1 50.6 43.7 43.6 30.0 26.4 26.0 21.1 24.6 28.3 0.0 Jul 25.7 38.6 30.2 29.3 31.5 38.6 49.0 60.4 38.4 36.5 27.2 24.5 20.5 19.2 23.0 23.2 0.0 Aug 22.1 26.7 25.1 25.9 30.6 33.2 55.4 44.6 41.1 32.0 43.6 20.2 19.0 17.8 27.4 21.1 0.0 Sep 27.8 27.8 29.7 27.6 36.0 37.2 40.2 70.0 42.7 32.1 34.9 23.9 21.7 21.3 27.8 25.0 0.0 Oct 27.4 33.0 29.9 32.8 40.6 39.0 41.5 75.5 41.2 33.8 34.4 20.2 20.7 26.6 26.4 22.9 0.0 Nov 26.7 29.7 27.7 32.3 36.3 40.3 52.0 57.1 35.0 33.7 29.5 23.0 20.3 22.3 25.1 27.6 0.0 Dec 29.1 28.0 29.5 35.0 36.7 38.0 43.9 50.0 37.9 33.6 27.5 24.6 22.9 27.5 28.7 24.9 0.0 Avg 26.3 30.3 29.3 30.8 34.5 38.3 44.3 54.7 45.8 37.1 31.7 24.0 21.8 21.8 25.0 26.3 0.0 30 The normalized data, from above, is adjusted for growth, using the Indexed Cumulative Growth. TrendModel: Trend 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 31. Growth-Adjusted Seasonal Factors Model 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 A C D E F G H I J K L M N O P Q R S X Growth-Adjusted Normalized Data: Factored Max Permitted Standard Deviations: 2.0 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 1.05 1.01 1.03 1.11 0.97 1.04 0.87 1.07 1.02 0.96 1.05 1.03 1.01 0.95 0.98 1.19 Feb 0.93 0.99 0.94 1.00 0.96 0.98 0.91 0.86 1.20 0.96 1.01 1.02 1.02 1.02 0.93 1.18 Mar 1.04 0.97 1.02 1.00 1.03 0.94 0.99 1.02 1.35 0.90 1.01 1.04 1.03 1.01 0.97 1.08 Apr 1.06 0.95 1.01 1.04 1.04 0.97 0.91 0.81 1.17 1.11 0.88 1.03 1.02 1.00 0.91 0.98 May 0.91 0.89 1.06 1.02 0.93 1.08 0.93 0.78 1.15 1.47 0.90 1.10 1.00 0.89 0.88 0.98 Jun 0.96 1.13 1.07 0.88 0.93 1.08 1.02 0.92 0.95 1.17 0.95 1.10 1.19 0.97 0.99 1.08 Jul 0.98 1.27 1.03 0.95 0.91 1.01 1.11 1.11 0.84 0.98 0.86 1.02 0.94 0.88 0.92 0.88 Aug 0.84 0.88 0.86 0.84 0.89 0.87 1.25 0.82 0.90 0.86 1.37 0.84 0.87 0.81 1.10 0.80 Sep 1.06 0.92 1.01 0.90 1.04 0.97 0.91 1.28 0.93 0.87 1.10 0.99 0.99 0.98 1.11 0.95 Oct 1.04 1.09 1.02 1.07 1.18 1.02 0.94 1.38 0.90 0.91 1.08 0.84 0.95 1.22 1.06 0.87 Nov 1.02 0.98 0.95 1.05 1.05 1.05 1.17 1.04 0.76 0.91 0.93 0.96 0.93 1.02 1.01 1.05 Dec 1.11 0.92 1.00 1.14 1.06 0.99 0.99 0.91 0.83 0.90 0.87 1.02 1.05 1.26 1.15 0.95 Avg 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 31 The growth-adjusted data is then expressed as an index. TrendModel: Trend 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 32. Growth-Adjusted Seasonal Factors Model 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 A C D E F G H I J K L M N O P Q R S X Y Z AA AB AC Growth-Adjusted Normalized Data: Factored Max Permitted Standard Deviations: 2.0 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Avg Std Dev Low High Wtd Avg Jan 1.05 1.01 1.03 1.11 0.97 1.04 0.87 1.07 1.02 0.96 1.05 1.03 1.01 0.95 0.98 1.19 1.02 0.07 0.88 1.17 1.03 Feb 0.93 0.99 0.94 1.00 0.96 0.98 0.91 0.86 1.20 0.96 1.01 1.02 1.02 1.02 0.93 1.18 0.99 0.09 0.82 1.17 0.97 Mar 1.04 0.97 1.02 1.00 1.03 0.94 0.99 1.02 1.35 0.90 1.01 1.04 1.03 1.01 0.97 1.08 1.03 0.10 0.83 1.22 1.01 Apr 1.06 0.95 1.01 1.04 1.04 0.97 0.91 0.81 1.17 1.11 0.88 1.03 1.02 1.00 0.91 0.98 0.99 0.09 0.81 1.17 1.01 May 0.91 0.89 1.06 1.02 0.93 1.08 0.93 0.78 1.15 1.47 0.90 1.10 1.00 0.89 0.88 0.98 1.00 0.16 0.68 1.32 1.00 Jun 0.96 1.13 1.07 0.88 0.93 1.08 1.02 0.92 0.95 1.17 0.95 1.10 1.19 0.97 0.99 1.08 1.02 0.10 0.83 1.21 1.02 Jul 0.98 1.27 1.03 0.95 0.91 1.01 1.11 1.11 0.84 0.98 0.86 1.02 0.94 0.88 0.92 0.88 0.98 0.11 0.76 1.20 0.97 Aug 0.84 0.88 0.86 0.84 0.89 0.87 1.25 0.82 0.90 0.86 1.37 0.84 0.87 0.81 1.10 0.80 0.92 0.17 0.59 1.26 0.89 Sep 1.06 0.92 1.01 0.90 1.04 0.97 0.91 1.28 0.93 0.87 1.10 0.99 0.99 0.98 1.11 0.95 1.00 0.10 0.80 1.21 1.01 Oct 1.04 1.09 1.02 1.07 1.18 1.02 0.94 1.38 0.90 0.91 1.08 0.84 0.95 1.22 1.06 0.87 1.03 0.14 0.75 1.32 1.02 Nov 1.02 0.98 0.95 1.05 1.05 1.05 1.17 1.04 0.76 0.91 0.93 0.96 0.93 1.02 1.01 1.05 0.99 0.09 0.81 1.17 1.00 Dec 1.11 0.92 1.00 1.14 1.06 0.99 0.99 0.91 0.83 0.90 0.87 1.02 1.05 1.26 1.15 0.95 1.01 0.12 0.78 1.24 1.07 Avg 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.11 0.78 1.22 1.00 Accepted Range 32 In order to determine what years we wish to exclude, each month’s factors are averaged, and an acceptable low & high range is calculated. TrendModel: Trend 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 33. Growth-Adjusted Seasonal Factors Model 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 A C D E F G H I J K L M N O P Q R S X Y Z AA AB AC Growth-Adjusted Normalized Data: Factored Max Permitted Standard Deviations: 2.0 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Avg Std Dev Low High Wtd Avg Jan 1.05 1.01 1.03 1.11 0.97 1.04 0.87 1.07 1.02 0.96 1.05 1.03 1.01 0.95 0.98 1.19 1.02 0.07 0.88 1.17 1.03 Feb 0.93 0.99 0.94 1.00 0.96 0.98 0.91 0.86 1.20 0.96 1.01 1.02 1.02 1.02 0.93 1.18 0.99 0.09 0.82 1.17 0.97 Mar 1.04 0.97 1.02 1.00 1.03 0.94 0.99 1.02 1.35 0.90 1.01 1.04 1.03 1.01 0.97 1.08 1.03 0.10 0.83 1.22 1.01 Apr 1.06 0.95 1.01 1.04 1.04 0.97 0.91 0.81 1.17 1.11 0.88 1.03 1.02 1.00 0.91 0.98 0.99 0.09 0.81 1.17 1.01 May 0.91 0.89 1.06 1.02 0.93 1.08 0.93 0.78 1.15 1.47 0.90 1.10 1.00 0.89 0.88 0.98 1.00 0.16 0.68 1.32 1.00 Jun 0.96 1.13 1.07 0.88 0.93 1.08 1.02 0.92 0.95 1.17 0.95 1.10 1.19 0.97 0.99 1.08 1.02 0.10 0.83 1.21 1.02 Jul 0.98 1.27 1.03 0.95 0.91 1.01 1.11 1.11 0.84 0.98 0.86 1.02 0.94 0.88 0.92 0.88 0.98 0.11 0.76 1.20 0.97 Aug 0.84 0.88 0.86 0.84 0.89 0.87 1.25 0.82 0.90 0.86 1.37 0.84 0.87 0.81 1.10 0.80 0.92 0.17 0.59 1.26 0.89 Sep 1.06 0.92 1.01 0.90 1.04 0.97 0.91 1.28 0.93 0.87 1.10 0.99 0.99 0.98 1.11 0.95 1.00 0.10 0.80 1.21 1.01 Oct 1.04 1.09 1.02 1.07 1.18 1.02 0.94 1.38 0.90 0.91 1.08 0.84 0.95 1.22 1.06 0.87 1.03 0.14 0.75 1.32 1.02 Nov 1.02 0.98 0.95 1.05 1.05 1.05 1.17 1.04 0.76 0.91 0.93 0.96 0.93 1.02 1.01 1.05 0.99 0.09 0.81 1.17 1.00 Dec 1.11 0.92 1.00 1.14 1.06 0.99 0.99 0.91 0.83 0.90 0.87 1.02 1.05 1.26 1.15 0.95 1.01 0.12 0.78 1.24 1.07 Avg 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.11 0.78 1.22 1.00 Data Accepted? 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Total Jan 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 Feb 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 Mar 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 Apr 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 May 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 Jun 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Jul 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Aug 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 Sep 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 Oct 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 Nov 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 Dec 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 OK? 1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 8 Use Std Dev? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Seasonal Factor Weights 1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 0 8 Accepted Range 33 A “Data Accepted?” table is added that flushes out those years where one or more months fall outside the accepted range. TrendModel: Trend 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 34. Growth-Adjusted Seasonal Factors Model 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 A C D E F G H I J K L M N O P Q R S X Y Z AA AB AC Growth-Adjusted Normalized Data: Factored Max Permitted Standard Deviations: 2.0 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Avg Std Dev Low High Wtd Avg Jan 1.05 1.01 1.03 1.11 0.97 1.04 0.87 1.07 1.02 0.96 1.05 1.03 1.01 0.95 0.98 1.19 1.02 0.07 0.88 1.17 1.03 Feb 0.93 0.99 0.94 1.00 0.96 0.98 0.91 0.86 1.20 0.96 1.01 1.02 1.02 1.02 0.93 1.18 0.99 0.09 0.82 1.17 0.97 Mar 1.04 0.97 1.02 1.00 1.03 0.94 0.99 1.02 1.35 0.90 1.01 1.04 1.03 1.01 0.97 1.08 1.03 0.10 0.83 1.22 1.01 Apr 1.06 0.95 1.01 1.04 1.04 0.97 0.91 0.81 1.17 1.11 0.88 1.03 1.02 1.00 0.91 0.98 0.99 0.09 0.81 1.17 1.01 May 0.91 0.89 1.06 1.02 0.93 1.08 0.93 0.78 1.15 1.47 0.90 1.10 1.00 0.89 0.88 0.98 1.00 0.16 0.68 1.32 1.00 Jun 0.96 1.13 1.07 0.88 0.93 1.08 1.02 0.92 0.95 1.17 0.95 1.10 1.19 0.97 0.99 1.08 1.02 0.10 0.83 1.21 1.02 Jul 0.98 1.27 1.03 0.95 0.91 1.01 1.11 1.11 0.84 0.98 0.86 1.02 0.94 0.88 0.92 0.88 0.98 0.11 0.76 1.20 0.97 Aug 0.84 0.88 0.86 0.84 0.89 0.87 1.25 0.82 0.90 0.86 1.37 0.84 0.87 0.81 1.10 0.80 0.92 0.17 0.59 1.26 0.89 Sep 1.06 0.92 1.01 0.90 1.04 0.97 0.91 1.28 0.93 0.87 1.10 0.99 0.99 0.98 1.11 0.95 1.00 0.10 0.80 1.21 1.01 Oct 1.04 1.09 1.02 1.07 1.18 1.02 0.94 1.38 0.90 0.91 1.08 0.84 0.95 1.22 1.06 0.87 1.03 0.14 0.75 1.32 1.02 Nov 1.02 0.98 0.95 1.05 1.05 1.05 1.17 1.04 0.76 0.91 0.93 0.96 0.93 1.02 1.01 1.05 0.99 0.09 0.81 1.17 1.00 Dec 1.11 0.92 1.00 1.14 1.06 0.99 0.99 0.91 0.83 0.90 0.87 1.02 1.05 1.26 1.15 0.95 1.01 0.12 0.78 1.24 1.07 Avg 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.11 0.78 1.22 1.00 Data Accepted? 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Total Jan 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 Feb 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 Mar 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 Apr 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 May 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 Jun 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Jul 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Aug 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 Sep 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 Oct 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 Nov 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 Dec 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 OK? 1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 8 Use Std Dev? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Seasonal Factor Weights 1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 0 8 Accepted Range 34 A weighted average is calculated, picking up all the accepted years. This is our goal: the growth-adjusted seasonal factors. TrendModel: Trend 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 35. 1 2 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 A F G H I Key Inputs None Initial Growth- Adjusted Jan-01 1.00 1.00 1.03 Feb-01 1.00 0.96 0.97 Mar-01 1.00 1.00 1.01 Apr-01 1.00 0.99 1.01 May-01 1.00 0.99 1.00 Jun-01 1.00 1.02 1.02 Jul-01 1.00 0.98 0.97 Aug-01 1.00 0.93 0.89 Sep-01 1.00 1.00 1.01 Oct-01 1.00 1.02 1.02 Nov-01 1.00 1.03 1.00 Dec-01 1.00 1.07 1.07 Jan-02 Seasonal Factors 1 2 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 A G H I J Calculations B. Seasonally-Adjusted Da In Use (1 = None; 2 = Initial; 3 = Final) : 2 None Initial "Final" In Use Jan-01 1.00 1.00 1.03 1.00 Feb-01 1.00 0.96 0.97 0.96 Mar-01 1.00 1.00 1.01 1.00 Apr-01 1.00 0.99 1.01 0.99 May-01 1.00 0.99 1.00 0.99 Jun-01 1.00 1.02 1.02 1.02 Jul-01 1.00 0.98 0.97 0.98 Aug-01 1.00 0.93 0.89 0.93 Sep-01 1.00 1.00 1.01 1.00 Oct-01 1.00 1.02 1.02 1.02 Nov-01 1.00 1.03 1.00 1.03 Dec-01 1.00 1.07 1.07 1.07 Seasonal Factors 1 195 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 A X Y Z AA AB AC Estimating Trend Growth-Adjusted Normalized Data: Factored Avg Std Dev Low High Wtd Avg Jan 1.02 0.07 0.88 1.17 1.03 Feb 0.99 0.09 0.82 1.17 0.97 Mar 1.03 0.10 0.83 1.22 1.01 Apr 0.99 0.09 0.81 1.17 1.01 May 1.00 0.16 0.68 1.32 1.00 Jun 1.02 0.10 0.83 1.21 1.02 Jul 0.98 0.11 0.76 1.20 0.97 Aug 0.92 0.17 0.59 1.26 0.89 Sep 1.00 0.10 0.80 1.21 1.01 Oct 1.03 0.14 0.75 1.32 1.02 Nov 0.99 0.09 0.81 1.17 1.00 Dec 1.01 0.12 0.78 1.24 1.07 Avg 1.00 0.11 0.78 1.22 1.00 Growth-Adjusted Seasonal Factors Model 35 Note that these final growth-adjusted seasonal factors are the set that are picked up in both the “Inputs” tab and “Calc” tab. TrendModel: Trend 1. Introduction 2. Inputs 3. Calc 4. Trend TrendModel: Inputs TrendModel: Calc
  • 36. Growth-Adjusted Seasonal Factors Model 36 We now turn to the chart that will be used to track our estimation of trend. TrendModel: Trend 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 49 50 51 52 53 54 55 56 57 58 59 60 61 62 Y Z AA AB AC AD AE AF AG AH AI AJ Seasonal Factors In Use: Initial 2 (1 = None; 2 = Initial; 3 = Final) 022.0 24.0 26.0 28.0 30.0 32.0 34.0 36.0 38.0 40.0 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Sales Volumes (Billions) NYSE Monthly Sales Volumes Seasonally-Adjusted Actual (& Extrapolated) Values Seasonally-Adjusted: Monthly Seasonally-Adjusted: 3-Mo Avg Estimated (& Extrapolated) Trend 1. Introduction 2. Inputs 3. Calc 4. Trend Model Structure: Chart
  • 37. Growth-Adjusted Seasonal Factors Model 37 One of the most important aspects for trending the data is the choice of seasonal factors to use. TrendModel: Trend 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 49 50 51 52 53 54 55 56 57 58 59 60 61 62 Y Z AA AB AC AD AE AF AG AH AI AJ Seasonal Factors In Use: Initial 2 (1 = None; 2 = Initial; 3 = Final) 22.024.026.028.030.032.034.036.038.040.0S N 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 38. Growth-Adjusted Seasonal Factors Model 38 Focusing on the chart, we start by setting the time range to the 1st three-four years of the series. TrendModel: Trend 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 39. Growth-Adjusted Seasonal Factors Model 39 Focusing on the chart, we start by setting the time range to the 1st three-four years of the series. TrendModel: Trend 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 40. Growth-Adjusted Seasonal Factors Model 40 The Actuals are the first set of data to chart. They are colored light gray to de- emphasize them; they’re here as an FYI. TrendModel: Trend 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 41. Growth-Adjusted Seasonal Factors Model 41 A dotted blue line is added, showing the seasonally-adjusted data. TrendModel: Trend 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 42. Growth-Adjusted Seasonal Factors Model 42 A thicker and solid blue line is added for the 3-month moving average on the seasonally-adjusted data. TrendModel: Trend 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 43. Growth-Adjusted Seasonal Factors Model 43 Finally, the Estimated Trend line is added to the chart, colored in red to emphasize its distinction. TrendModel: Trend 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 44. Growth-Adjusted Seasonal Factors Model 44 The heart of the estimation trend analysis is performed at the top of the “Trend” tab. TrendModel: Trend 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 49 50 51 52 53 54 55 56 57 58 59 60 61 62 A C D E F G H I J K L M N O P Q R S X Y Z AA AB AC AD AE AF AG AH AI AJ Estimating Trend Seasonal Factors In Use: Initial 2 (1 = None; 2 = Initial; 3 = Final) Growth Rate 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Feb 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Mar 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Apr 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% May 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Jun 2.0% 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Jul 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Aug 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Sep 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% Oct 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0% Nov 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0% Dec 2.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.0% 0.0% Start 25.0 Events 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Jan Feb 2.0% Mar Apr May Jun Jul 10.0% Aug Sep 30.0% Oct -20.0% Nov Dec Actuals vs Estimate by Year 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Actual 307.5 363.1 352.4 369.6 415.1 458.5 532.0 660.3 549.3 444.7 383.9 286.8 260.7 261.9 299.1 315.5 0.0 Est 306.4 336.0 357.3 361.9 365.6 366.9 371.3 376.8 378.9 382.9 387.9 389.9 393.1 398.7 402.4 407.4 413.8 Diff -1.1 -27.1 4.9 -7.7 -49.4 -91.6 -160.8 -283.5 -170.4 -61.8 4.1 103.1 132.4 136.8 103.3 91.9 % Diff -0.3% -7.5% 1.4% -2.1% -11.9% -20.0% -30.2% -42.9% -31.0% -13.9% 1.1% 35.9% 50.8% 52.2% 34.5% 29.1% Total 2001-16 YTD Actual 6,260 315.5 Est 5,983 407.4 Diff (277) 91.9 % Diff -4.4% 29.1% 022.0 24.0 26.0 28.0 30.0 32.0 34.0 36.0 38.0 40.0 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Sales Volumes (Billions) NYSE Monthly Sales Volumes Seasonally-Adjusted Actual (& Extrapolated) Values Seasonally-Adjusted: Monthly Seasonally-Adjusted: 3-Mo Avg Estimated (& Extrapolated) Trend 1. Introduction 2. Inputs 3. Calc 4. Trend
  • 45. Growth-Adjusted Seasonal Factors 45 We now start the process of estimating trend, using a chart and table that focuses on 3-4 years of time. 1. Introduction 2. Model Structure 3. Estimating Trend 4. Modifying Trend 5. Final Notes TrendModel: TrendEstimating Trend 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 49 50 51 52 53 54 55 56 57 58 59 60 61 62 A C D E F X Y Z AA AB AC AD AE AF AG AH AI AJ Estimating Trend Seasonal Factors In Use: Initial 2 (1 = None; 2 = Initial; 3 = Final) Growth Rate 2001 2002 2003 2004 Jan 2.0% 2.0% 1.0% 1.0% Feb 2.0% 2.0% 1.0% 1.0% Mar 2.0% 2.0% 1.0% 1.0% Apr 2.0% 2.0% 1.0% 1.0% May 2.0% 2.0% 1.0% 1.0% Jun 2.0% 2.0% 1.0% 1.0% Jul 2.0% 1.0% 1.0% 1.0% Aug 2.0% 1.0% 1.0% 1.0% Sep 2.0% 1.0% 1.0% 1.0% Oct 2.0% 1.0% 1.0% 1.0% Nov 2.0% 1.0% 1.0% 1.0% Dec 2.0% 1.0% 1.0% 1.0% Start 25.0 Events 2001 2002 2003 2004 Jan Feb Mar Apr May Jun Jul 10.0% Aug Sep 30.0% Oct -20.0% Nov Dec Actuals vs Estimate by Year 2001 2002 2003 2004 Actual 307.5 363.1 352.4 369.6 Est 306.4 336.0 357.3 361.9 Diff -1.1 -27.1 4.9 -7.7 % Diff -0.3% -7.5% 1.4% -2.1% 022.0 24.0 26.0 28.0 30.0 32.0 34.0 36.0 38.0 40.0 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Sales Volumes (Billions) NYSE Monthly Sales Volumes Seasonally-Adjusted Actual (& Extrapolated) Values Seasonally-Adjusted: Monthly Seasonally-Adjusted: 3-Mo Avg Estimated (& Extrapolated) Trend
  • 46. Chapter 6: Seasonal Factors Growth-Adjusted Method 46 Original Data Holiday Factors Normalized Data Seasonal Factors (Monthly Factors) Seasonally- Adjusted Data: Initial Seasonally- Adjusted Data: Initial Growth Rate (Adjustments) Events (Adjustments) Seasonally- Adjusted Data: Final Equated Day Factors (Day of Week)
  • 47. Seasonal Factors: Growth-Adjusted Method 47 In Chapter 5 we developed seasonal factors using a method that relied almost solely on calculations alone; only a quick review afterwards was needed to help verify reasonableness. Now we come to developing seasonal factors using the more involved “Growth-Adjusted Method”. I would generally recommend this method, especially if you’re keen to learn from your history. This method will enable you to: 1. Measure impact of marketing campaigns. 2. Develop alternative estimates that may support other estimates using different approaches: if the different methods arrive at the same result, much confidence is gained; if results differ, you have reason to research why – and learn from it. 3. Measure impact of new product launch – on total sales, and on sales of existing products. 4. Estimate price elasticity. 5. Identify and quantify shifts soon after they occur. Introduction
  • 48. Seasonal Factors: Growth-Adjusted Method 48 This is a fundamental and critical question. The idea behind “seasonal factors” is that they measure predictable variability across the year, based entirely on the time of year alone. We want to know how much busier or quieter a metric will be during April or October solely because it is April or October. Business variability due to the length of the month was addressed by normalizing the data. We wish to answer the question: all else being equal (price levels, product availability, general economy, weather, etc.), how much busier or quieter is it because it’s April or October? To illustrate, suppose you have a business with constant growth, like the 10% annual rate of growth depicted in Chart 6.1? If we take the data “as is”, without adjusting for growth, we will have seasonal factors looking like those in Chart 6.2, which shows December is almost 9% busier than January. Why Adjust for Growth? 1. Construct “Inputs” tab 2. Construct “Calc” tab 3. Construct “Trend” tab 4. Run Preliminary Trend 5. Run Final Trend Chart 6.1: XYZ’s Constant Growth Chart 6.2: XYZ’s Seasonal Factors It may be difficult to make out from the chart, but all 4 years have the same identical pattern.
  • 49. Seasonal Factors: Growth-Adjusted Method 49 Were we to apply these seasonal factors to the original data, with January numbers increased and December numbers decreased, we arrive at the series of step functions displayed in Chart 6.3. Seasonally-adjusting the data has stripped out all the growth, resulting in a pattern of flat growth punctuated by 10% bumps every January. Its pretty apparent that seasonalizing the data here gives us a false picture of how business is behaving. Growth should be constant, not flat; the problem is that the seasonal factors include the growth. In order for the seasonally-adjusted data to capture correctly the “true” pattern of consistent growth we need to make sure we adjust for growth when developing the seasonal factors. In effect, we want the seasonal factors to look like the dotted bold green line in Chart 6.4. Why Adjust for Growth? (cont.) 1. Construct “Inputs” tab 2. Construct “Calc” tab 3. Construct “Trend” tab 4. Run Preliminary Trend 5. Run Final Trend Chart 6.4: XYZ’s “True” Seasonal FactorsChart 6.3: XYZ Sales, Seasonally-Adjusted
  • 50. Seasonal Factors: Growth-Adjusted Method 50 When our seasonal factors are adjusted for growth, resulting here in a flat “zero” seasonality, we end up with a seasonally-adjusted line in Chart 6.5 that is identical to the original data. This is as it should be for as constructed in our idealized original, there is no seasonality, there is no pattern of consistent fluctuation across the year. 1. Construct “Inputs” tab 2. Construct “Calc” tab 3. Construct “Trend” tab 4. Run Preliminary Trend 5. Run Final Trend Chart 6.5: XYZ Sales, Seasonally-Adjusted Obviously, data never behaves so smoothly and “perfectly” as this. We simplified it to illustrate an essential point: when data is not adjusted for growth, the consequent seasonal factors that are developed will fail to capture the pattern across the year that is solely due to seasonality alone; instead it will mistakenly include growth, and thereby distort how the underlying data is truly behaving. If growth was an absolute constant, that wouldn’t be a problem; but that is rarely, if ever, the case. Why Adjust for Growth? (cont.)
  • 51. 51 The basic approach for the Growth-Adjusted Method involves five main steps: 1. Start with normalized data (already adjusted for calendar effect). 2. Estimate growth rates and events over the given period. 3. Calculate the cumulative growth rate by month, including events. 4. Adjust the normalized data for the cumulative growth, and express as an index. 5. Calculate standard deviations, and remove outlier data. Approach No. Action Description 1 Construct “Input” section “Input” tab collects key data from outside sources; it can be easily updated. 2 Construct “Calc” section “Calc” tab is where almost the calculations for the model are performed. 3 Construct “Trend” section Basic framework is established for trending the data, including chart. 4 Run Preliminary Trend A first set of trend estimates are manually input into “Trend” tab. 5 Run Final Trend Model is updated to use the model’s estimate of seasonal factors; the trend estimates are tweaked using the new & improved factors. This Growth-Adjusted technique is described in detail in Appendix C, How to Develop Growth-Adjusted Seasonal Factors. Look to this appendix for explanation of the how and why these factors can be developed. In these summary pages, we will highlight the main features and process. Seasonal Factors: Growth-Adjusted Method
  • 52. 1 2 7 8 9 10 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 609 610 611 612 613 614 615 616 617 618 619 620 621 622 A B C D E Key Inputs Linked to diff file Avg Days per Mo (1970-97): 20.73 Avg Days per Mo (1998-2020): 20.69 Actuals No. of Days Norm Factor Seas Factor (Short Method) Jan-00 21,484,254,618 20.4 0.99 1.02 Feb-00 20,917,632,140 19.8 0.96 0.99 Mar-00 26,182,766,564 23.1 1.12 1.00 Apr-00 20,140,405,405 18.9 0.91 0.99 May-00 19,919,341,288 21.7 1.05 0.99 Jun-00 21,703,321,017 22.1 1.07 1.02 Jul-00 19,076,891,454 19.1 0.92 0.96 Aug-00 20,379,201,651 23.1 1.12 0.88 Sep-00 20,825,856,353 19.8 0.96 1.00 Oct-00 25,972,211,976 21.6 1.04 1.07 Nov-00 21,700,515,606 20.4 0.98 1.00 Dec-00 24,175,307,011 18.6 0.90 1.07 Jan-01 27,844,005,557 21.9 1.06 1.02 Feb-01 21,631,058,254 18.8 0.91 0.99 Mar-01 27,970,177,009 22.0 1.07 1.00Jan-19 0 21.1 1.02 1.02Feb-19 0 18.8 0.91 0.99Mar-19 0 21.0 1.02 1.00Apr-19 0 20.8 1.01 0.99May-19 0 21.8 1.05 0.99Jun-19 0 20.0 0.97 1.02Jul-19 0 21.2 1.03 0.96Aug-19 0 21.9 1.06 0.88Sep-19 0 19.8 0.96 1.00Oct-19 0 22.7 1.10 1.07 Nov-19 0 19.3 0.93 1.00 Dec-19 0 19.4 0.94 1.07 Jan-20 0 21.3 1.03 1.02 Feb-20 0 18.8 0.91 0.99 Mar-20 0 21.9 1.06 1.00 Apr-20 0 20.9 1.01 0.99 May-20 0 19.7 0.95 0.99 Jun-20 0 22.2 1.07 1.02 Jul-20 0 21.8 1.05 0.96 Aug-20 0 20.9 1.01 0.88 Sep-20 0 20.7 1.00 1.00 Oct-20 0 21.8 1.05 1.07 Nov-20 0 19.2 0.93 1.00 Dec-20 0 20.3 0.98 1.07 Seasonal Factors: Growth-Adjusted Method 52 Table 6.1 captures some of the key pieces of data we will be using for trending NYSE sales. The Actuals (Col. B) are captured here, as well as previously developed month lengths (Col. C) and seasonal factors (Col. E). Column D calculates the normalization factors, representing each month’s length as an index, where the length is compared with the average month length over the entire period, not just compared to each individual year’s length. Why? Because some years are longer or shorter than others due to whether the 365th day falls on a weekday or weekend, leap year, events – e.g. the NYSE was closed 4 days after 9/11, 2 days for Hurricane Sandy, etc. Construct “Inputs” tab 1. Construct “Inputs” tab 2. Construct “Calc” tab 3. Construct “Trend” tab 4. Run Preliminary Trend 5. Run Final Trend Table 6.1: Inputs Inputs The overall 1970-2020 period is split in two here because of the addition of the Martin Luther King holiday, starting in 1998. Note that the entire 1970-2020 period was split in two because the years 1998-on came in slightly lower than previously, due to the markets being closed for Martin Luther King Day, starting in 1998. Also note that 2001 was removed from the 1998- 2020 average calculation: it was the only year that had so many additional closures - the NYSE was shut 4 days following the 9/11 attacks.
  • 53. Seasonal Factors: Growth-Adjusted Method 53 The “Calc” tab is the place where virtually all the calculations are performed. Table 6.2 below shows the entire set of calculations that we make with the NYSE data. These calculations are divided into five sections which are fully described in the Appendix. A summary: Construct “Calc” tab: What Performed Here 1. Construct “Inputs” tab 2. Construct “Calc” tab 3. Construct “Trend” tab 4. Run Preliminary Trend 5. Run Final Trend Table 6.2: Calc tab Calc Section Activity Description A Actual & Normalized Data Place for manual data adjustments to be inserted (Col. C); adjusted actuals are then normalized (Col. F). B Seasonally-Adjusted Data Seasonal factor estimates are brought in – whatever already available (Col. G) and then those to be calculated in the “Trend” tab (Col. H). Normalized data is then seasonally-adjusted (Col. J), and smoothed (Col. K). C Estimated Trend Picks up your estimates of growth & events (Col. L, M) – performed in “Trend” tab; calculates trend using those estimates (Col. N). “Trend” is the smoothed line; “Values” have the “noise” of calendar & seasonality put back in. D Forecasts Calculates forecasts, by growing the prior period trend value using your estimates of “Growth” & “Events”. E Other Additional miscellaneous calculations that may be useful for reference or charting purposes. 1 2 7 8 9 10 371 372 373 557 558 559 560 561 562 563 564 565 A B C D E F G H I J K L M N O P Q R S T Calculations Unit: 0.000000001 (Billions) In Use: 1 Start: 20.000 Actuals Adjust- ments Adjusted Actuals Normalization Factors Normalized Data Initial Growth- Adjusted In Use Seasonally- Adjusted: Monthly Seasonally- Adjusted: 3- Mo Avg Growth Rate 1-Time Events Estimated Trend Estimated Trend Values Extrapolated Trend Extrapolated Trend Values (= Forecast) Estimated (& Forecast) Trend Actual (& Forecast) Values Estimate vs Actual: Diff Jan-00 21.484 21.484 0.99 21.754 1.02 0 1.02 21.417 20.577 15.0% 0.0% 20.250 20.313 20.250 21.484 (1.234) Feb-00 20.918 20.918 0.96 21.874 0.99 0 0.99 22.139 22.304 15.0% 0.0% 20.503 19.372 20.503 20.918 (0.415) Mar-00 26.183 26.183 1.12 23.452 1.00 0 1.00 23.356 22.559 15.0% 0.0% 20.759 23.272 20.759 26.183 (5.423)Jul-14 20.238 20.238 1.05 19.219 0.96 0 0.96 19.919 20.159 5.0% 0.0% 21.203 21.542 21.203 20.238 0.965Aug-14 17.852 17.852 1.01 17.704 0.88 0 0.88 20.074 20.477 5.0% 0.0% 21.291 18.934 21.291 17.852 3.440Sep-14 21.684 21.684 1.01 21.533 1.00 0 1.00 21.437 22.166 5.0% 5.0% 22.449 22.708 22.449 21.684 0.765Oct-14 29.250 29.250 1.10 26.571 1.06 0 1.06 24.988 22.883 5.0% 0.0% 22.543 26.387 22.543 29.250 (6.707)Nov-14 19.750 19.750 0.88 22.418 1.01 0 1.01 22.224 24.168 5.0% 0.0% 22.637 20.117 22.637 19.750 2.887Dec-14 26.228 26.228 0.98 26.898 1.06 0 1.06 25.291 23.861 5.0% 0.0% 22.731 23.573 22.731 26.228 (3.497)Jan-15 23.907 23.907 0.98 24.447 1.02 0 1.02 24.069 24.403 5.0% 0.0% 22.826 22.672 22.826 23.907 (1.235)Feb-15 21.359 21.359 0.91 23.566 0.99 0 0.99 23.851 23.975 5.0% 0.0% 22.921 20.526 22.921 21.359 (0.833)Mar-15 25.555 25.555 1.06 24.105 1.00 0 1.00 24.007 23.509 5.0% 0.0% 23.016 24.500 23.016 25.555 (1.055)Apr-15 22.758 22.758 1.01 22.522 0.99 0 0.99 22.670 22.925 5.0% 0.0% 23.112 23.201 23.112 22.758 0.444May-15 20.907 20.907 0.95 21.909 0.99 0 0.99 22.098 22.961 5.0% 0.0% 23.208 21.958 23.208 20.907 1.050Jun-15 26.087 26.087 1.06 24.605 1.02 0 1.02 24.116 23.402 5.0% 0.0% 23.305 25.210 23.305 26.087 (0.877) Jul-15 24.478 24.478 1.06 23.149 0.96 0 0.96 23.992 26.425 5.0% 0.0% 23.402 23.877 23.402 24.478 (0.602) Aug-15 27.811 27.811 1.01 27.489 0.88 0 0.88 31.168 27.656 5.0% 20.0% 28.200 25.163 28.200 27.811 (2.649) Sep-15 28.009 28.009 1.00 27.933 1.00 0 1.00 27.808 29.667 5.0% 0.0% 28.317 28.522 28.317 28.009 0.513 Oct-15 33.580 33.580 1.05 31.926 1.06 0 1.06 30.024 28.223 5.0% 0.0% 28.435 31.802 28.435 33.580 (1.778) Nov-15 25.159 25.159 0.93 27.070 1.01 0 1.01 26.835 28.551 5.0% 0.0% 28.554 26.770 28.554 25.159 1.611 Dec-15 30.015 30.015 0.98 30.621 1.06 0 1.06 28.792 28.526 5.0% 0.0% 28.673 29.891 28.673 30.015 (0.124) Jan-16 28.688 28.688 0.94 30.422 1.02 0 1.02 29.951 29.372 5.0% 0.0% 28.792 27.578 28.792 28.688 (1.110) Feb-16 0 0 0.95 0 0.99 0 0.99 5.0% 0.0% 28.912 27.177 28.912 27.177 0 Mar-16 0 0 1.06 0 1.00 0 1.00 5.0% 0.0% 29.033 30.868 29.033 30.868 0 D. Forecasts E. Other Seasonal Factors A. Actual & Normalized Data B. Seasonally-Adjusted Data C. Estimated Trend
  • 54. Seasonal Factors: Growth-Adjusted Method 54 A crucial step in growth-adjusting the data is the insertion of estimates of growth. These estimates should be broken out into at least two separate groupings: the “Growth Rate” that captures the underlying longer-term growth (or decline) of the data, and the “Events” that capture the shifts that periodically occur (& usually constitute most of what is labeled as “growth”). Table 6.3 illustrates what these look like, with periodic changes in the growth rate highlighted using conditional formatting, and 1-time event estimates captured in a separate table (Rows 31-42). Construct “Trend” tab 1. Construct “Inputs” tab 2. Construct “Calc” tab 3. Construct “Trend” tab 4. Run Preliminary Trend 5. Run Final Trend The numbers developed here are illustrative. Accurate estimation of growth rates and events is an iterative process. For now we are focused on developing growth-adjusted seasonal factors (GASF); the values here will be used to show how we develop those GASFs. In the next chapter, we will turn our attention to “Estimating Trend” and specifically developing more appropriate values than those shown here. Table 6.3: Illustration of Growth & Event Estimates Trend 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 A C D E F G H I J K L M N O P Q R S T U Estimating Trend Growth Rate 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 Jan 15.0% 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 5.0% 2.0% 0.0% Feb 15.0% 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 5.0% 2.0% 0.0% Mar 15.0% 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 5.0% 2.0% 0.0% Apr 15.0% 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 2.0% 2.0% 0.0% May 15.0% 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 2.0% 2.0% 0.0% Jun 15.0% 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 2.0% 2.0% 0.0% Jul 15.0% 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% 5.0% 5.0% 2.0% 2.0% 0.0% Aug 15.0% 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% 5.0% 5.0% 2.0% 2.0% 0.0% Sep 15.0% 15.0% 0.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 5.0% 2.0% 2.0% 0.0% Oct 15.0% 15.0% 0.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 5.0% 2.0% 2.0% 0.0% Nov 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 5.0% 2.0% 2.0% 0.0% Dec 15.0% 15.0% 0.0% 0.0% 10.0% 10.0% 10.0% 10.0% -5.0% -5.0% -8.0% -8.0% -8.0% -8.0% 5.0% 5.0% 2.0% 2.0% 0.0% Start 20.0 1-Time Events 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 Jan Feb Mar Apr -15.0% May -35.0% Jun Jul 10.0% Aug -15.0% 20.0% Sep 25.0% 5.0% Oct Nov 10.0% Dec Conditional formatting is applied to highlight when growth rates (Rows 11-22) change.

Editor's Notes

  1. This chapter describes the model to be used for estimating trend and developing the final, growth-adjusted seasonal factors. The focus of this chapter will be the model structure, an explanation of why and how it works the way it does. The next chapter will walk through the trend estimation process itself which culminates in the final growth-adjusted seasonal factors.
  2. This chapter walks through the structure of the Trend Model. It begins with an introduction reviewing why we need to adjust the data for growth before arriving at a final set of seasonal factors. The chapter then walks through the three basic parts of the trend model: the Inputs, the Calculations, and the Trending.
  3. Why do we need to adjust the data for growth and events before we calculate seasonality? The importance of adjusting growth is apparent in this simple example. Here there is some seasonality across the year, with summer busier than the rest of the year. But notice how because of growth, December (as well as October & November) is consistently busier than January (& February). If you were to estimate seasonality without adjusting for the growth you would falsely conclude December is significantly busier than January.
  4. Here you can see how the data behaves when growth is taken away. Note how January & December in Year 2 are at a much more similar level – no longer does December come in much higher than January, thanks to our adjusting the data for growth.
  5. We also need to adjust for events. Here we have a 15% bump in September that we would want to adjust for. The adjustment would reduce the last 4 months of this year by the 5% bump. Just as with growth, adjusting for events helps ensure the measured seasonal pattern captures fluctuation across the typical year that is due to seasonality alone.
  6. Once the data has been adjusted for growth & events, as well as the calendar effect, we have a clearer picture of the “true” seasonal pattern across the year. It’s quite striking how much cleaner the pattern is after adjusting for growth & events. Obviously I acknowledge that rarely will the pattern each year be as clear and steady as it is here. “Noise” was much reduced for this hypothetical dataset in order to help clarify the necessity of adjusting for growth, & events.
  7. The Growth-Adjusted Seasonal Factors Model is divided into three parts, laid out over three tabs. The “Inputs” tab draws data in from other files that will be used in the model. This is also the section where each new month of data would be added. The “Calc” tab performs most of the calculations in the model. Except for monthly updates, it should never require revision. The “Trend” tab is the heart of the model; it is where the trend estimates are manually input, as well as where the final seasonal factors are calculated, the factors that will be growth-adjusted.
  8. The “Inputs” tab draws in the key data, generally brought in from other files. This is where you bring in Actuals, and where new updates come in. It is also where the normalization factors are brought in, as you can see from the table here. Note that the normalization factors go through 2020 – you’ll want these at hand when you develop your forecasts.
  9. The initial seasonal factors, calculated in the last chapter, are brought in. For clarity, I also have the other two sets of seasonal factors here, so they are all in one place. The set of factors labeled “None” here is where there is no seasonality, so all the factors are simply 1.00. This is a set you may want to try if you want to see how the normalized data looks without adjusting for any seasonality. The “Final” set of factors here will later be determined in the “Trend” tab. This is all I’ve placed in the “Inputs” tab. But be aware the Inputs tab is a place where you’ll want to park other outside info that you may want to work with as you trend and analyze your data – info such as economic data, or competitor info, or price changes, or whatever.
  10. The “Calc” tab is where most of the calculations take place. It is designed to never need changing or tweaking; that’s all done in the “Trend” tab. The exception is that each month some formulas are copied down so that the model updates in a way that keeps the Trend chart “clean” – we’ll see what I mean when we later walk through the “Trend” tab. The display of the tab here shows the 1st year of calculations, then hides everything until July 2016. Ordinarily, all the months are on full display. I’ve formatted this way of course, so you can see what is going on at the start & finish of the time period; all the “hidden” months have the same formulas as those visible here. As you can see, the “Calc” tab is split into five sections. We’ll now walk through each of these sections to explain what they are about.
  11. The “Actual & Normalized Data” section brings in the original actuals from the “Inputs” tab. An “Adjustments” column (Col C) has been inserted. Why? Because I’ve found on occasion that sometimes you need to perform a manual adjustment to the data, often necessary due to accounting issue. Perhaps the data for the last day or so of the month came in too late to be counted so one month is artificially a bit low and the subsequent month too high. This issue can be obvious on a chart when you see a low spike one month, and a high spike the next, or vice versa. If you can get accounting to fix it great, but often you can’t, so this column is a place to insert a manual modification. But try and be sure to have your adjustments add to exactly zero, unless you know the grand totals for your firm are running lower than the correct amount. The adjustments are added (or subtracted) form the original data to arrive at adjusted data, which is then normalized using the normalization factors brought in from the “Inputs” tab.
  12. The “Seasonally-Adjusted Data” section calculations the seasonally-adjusted amount for each month. As you can see, though, it has 3 different sets of seasonal factors to choose from. Which set is to be used is decided in the “Trend” tab; this tab just brings in your selection and assigns the appropriate set of factors to use. The three sets are as follows: “None” is the assumption that there is no seasonality; every month has the factor 1.00. “Initial” is the set of Initial Seasonal Factors, as was described in the last chapter. This column could be used for any possible set of factors that you want to work with initially. As we mentioned earlier, you could pick up your developed factors for Product A, to apply as a useful starting point for Product B. The “Final” seasonal factors, in Column I, are brought in from the “Trend” tab. Note that the values are in blue format; this is my way of recognizing the values that will be coming in from the “Trend” tab. Column J shows the seasonal factors that are being used. The highlighted Cell J8 at the top identifies the chosen seasonal factor set. Again, this choice is made on the “Trend” tab; the number determining which set of factors will be picked up by formula. Column K is the desired seasonally-adjusted amount; it is calculated by simply dividing the Normalized Data (from Column F) by the chosen Seasonal Factor (from Column J). Finally, Column L is a running 3-month average. As we’ll see when we chart the data in the “Trend” tab, this smooths the data and can help determine the general trend and behavior. Note that these last 2 columns are blank from January 2017-on. This is so the chart stops with the last full month of data that is available, and so the chart doesn’t plunge to zero in January because there is no data yet for that month.
  13. This next section of the “Calc” tab calculates the estimated trend. Let’s be clear about what is meant by “trend” here. The “trend” is a rough approximation of how the data is behaving over time. Even after seasonal adjustment, data will show a fair amount of noise. The trend endeavors to cut through that noise and identify the approximate behavior or trend. You’ll better see what is meant by this when we include the estimated trend in our chart on the “Trend” tab. The trend estimate has two components: growth rate and events. The “growth rate” describes the slope of the data on an annual basis; “events” describe the step functions that occur. Estimates of growth rate & events are performed, manually, in the coming “Trend” tab. The formulas here pick up those trend component estimates. The values shown here are placeholders; they will be changed when we later walk through the trend estimation process. Notice the highlighted “Start” value in Cell O8. This is an initial rough estimate of the level the data is at as we begin this process. This estimate will also be subject to change when we walk through the estimation process. Each month’s estimation trend amount picks up the prior month, and then “adds on” growth & events. Thus, for January 2001, we start off with the initial 25 million estimate and add to it an annual growth rate of 2.0%. We only want to add on one month of growth so we multiply the starting value of 25 by the 2.o% growth rate, and get 0.5 million; we then divide that by 12 to get 0.042, which when added to the initial 25.0 gives us a total of 25.042. And so on each month. Occasionally there will be events – these are treated differently in that they are taken whole. So in September 2001, the starting amount of 25.335 million is grown by the 2% annual rate, and then an additional 30% is added, bringing us to the much higher 32.991 million shown here in Cell O19. The last column here is the “Estimated Trend Values”. This column takes our Estimated Trend (from Column O), and puts back in the noise of the calendar effect and seasonality. Why bother with this? Because it is absolutely essential that our estimated trend line is at the approximate same level as the actuals, in the long run. Each month the estimated trend is going to be a bit above or below the actuals; we want to make sure that over time the lower and higher amounts offset one another, such that the total actuals and total estimates are almost the same. However, the comparison will be made with the estimated trend values rather than the simple estimated trend itself. Although the estimated trend is a simplified line describing how the data is behaving over time, it is still ultimately describing how the data behaves with the noise put back in. We want the actuals, with all their noise, and the estimated trend values, with its noise, to approximately match in the long run. How are the estimated trend values calculated? By picking up the estimated trend amount from Column O and multiplying it by the Normalization Factor (from Column E) and the Seasonal Factor in use (from Column J).
  14. The 4th section is where the forecasts are calculated. The values here do not “start” until the 1st month for which we do not have data; thus the column is blank until January 2017. The forecast trend is labeled here as “extrapolated” trend. Why change the name? Because in some organizations, the person or department running this model may not be the same as the department responsible for the “official” forecast. Perhaps the Sales department is on the hook for that, and perhaps you’re in the Financial Analysis area, so you aren’t responsible for the official forecast. Instead, others look to you to help understand how the data is trending (at least they certainly should be looking to you for that). When you are generating projections of trend and trend values, you want it to be clear your figures are not official and not meant to replicate what the Sales department is putting together. I have found it useful to clarify the distinction by referring to the projections from this model as “extrapolated” trend and “extrapolated” trend values. The numbers here are derived in the exact same way as the estimated trend and estimated trend values. Thus, the extrapolated trend takes the prior month’s trend and adds to it using the estimates of growth rate and events. The formula makes sure that in the very 1st month, the extrapolated trend picks up the prior month’s trend from Column O; in subsequent months, it will pick up from Column Q. Meanwhile the extrapolated trend values take the extrapolated trend and multiply them by the noise of the calendar effect and seasonality.
  15. The 5th and final section picks up past & future values and puts them all in one column. Thus, for trend in Column S, it picks up the estimated trend from Column O up through December 2016, then shifts over to extrapolated trend from January 2017 on. Meanwhile, in Column T, past actuals are picked up from Column B and extrapolated trend values from January 2017 forward are picked up from Column R. Why do this? It all has to do with the charting that we’ll see on the “Trend” tab. Rather than have two separate lines, one for the past and one for the future, we have one line describing past & future combined; and then we’ll superimpose a yellow background to distinguish the past from the forecast.
  16. Before we leave the “Calc” tab, I want to point out that there are annual totals calculated at the foot of the tab. These simply sum up the totals for each year. Note however, that the totals for some of the columns have a grey background. That’s because these are averages for each year, rather than a sum. The average Normalization Factors in 2001 was 0.983 (while the sum total would be a bit under 12). The average seasonal factors are exactly 1, and always should be, by definition. The average growth rate in 2001 is 2.0% - every month used that rate, while future years have lower rates in place (though again, these will all be changing dramatically when we walk through estimating the trend line). Note that the 1-Time Events are a simple sum, as that more closely describes their effect – while each month’s growth rate is divided by 12, the event estimates are taken whole. And with that we’re done with describing the “Calc” tab. Again, this tab will rarely be used going forward. It’s where almost all the calculations are taking place, to be sure. But except for monthly updates for charting purposes (which we’ll later walk through), we won’t need to look at this tab again.
  17. We now move on to the “Trend” tab. This table shows the entire tab, which can be broken out into three sections. Although the Seasonal Factors Calculation is the largest section, once it is set up there is little to do with it (just like the “Calc” tab). Indeed, you may want to park it on a separate tab. I’ve kept it here out of habit, and as I find it helpful to see what’s going on down below. But the heart of this tab is the Trend Estimates and accompanying chart. Let’s walk through each of the three sections in turn.
  18. The Trend Estimate section is the primary driver of this trend model. This is where you input your estimates of trend, expressed in terms of the growth rate and events. It is also where you can compare how well your estimated trend line matches up with the running total for the actuals. This image shows the entire 2001-17 period. We really don’t need to see all these years together, so going forward we’ll just focus on the 1st 4 years, from 2001-04. And, we’ll key in on the month of September 2001 to observe more closely how the model works.
  19. Let’s look at the Growth Rate section. Three points to make here. 1st, the growth rates are annual, i.e. each month’s growth rate is the estimate of the annual growth rate at that time. The growth rates here, which are just placeholders for the moment, indicate the sales are growing at an annual rate of 2.0% from January 2001 thru June 2002; the rate drops the following month to 1.0%. 2nd, the growth rate is conditionally formatted, with an outline & yellow fill, whenever the growth rate changes; that’s why July 2001’s rate is highlighted, as well as our beginning rate in January 2001. 3rd, the growth rate is expressed at the 1/10 of 1% level. I’ve almost always found this is the most appropriate level of precision to work at. Rarely will you be able to be more precise (& use 1/100 of 1%). And usually you can at least get the growth rate accurate to perhaps a ½% level; i.e., you can express the rate as 1.5%, or 1.0 or 2.0%; being more precise, such as 1.7%, risks suggesting a level of accuracy that is usually absent.
  20. The Starting Point is your estimate of what level the data is at as the model begins to trend the data. This model is for the period 2001-Present. Thus, the starting point here is for the level as the year 2001 begins. It has been estimated here at 25.0 billion, though we’ll later be playing with this (& the growth rates & events) when we walk through estimating trend.
  21. Events are those occasions where the level suddenly & significantly shifts up or down. Most months do not have events. Indeed, if you have an event every other month or so, you risk just following the data around wherever it’s going and you lose a sense of how the data is trending over time. We can see that September 2001 has a 30% event input. Of course, that’s the month of 9/11, so not surprisingly the sales shot up that month. There is a -20% drop shown here for October 2001. This is just a placeholder, but it suggests that much of the September spike is a one-off, that sales soon drop back closer to their prior level. On the other hand, we see a 10% increase in July 2002. This indicates a shift that is “permanent”, an increase that is held for a long period of time.
  22. The Actuals vs Estimate section performs a very important function: it compares how your estimates line up with actuals. Ideally, the estimates and actuals will be almost identical. They won’t exactly match, but they should be close. I try to maintain a difference of less than one-half of one percent each year. That way I know I’m not far off in any given year. That while the estimated trend line may be above or below the seasonally-adjusted actuals for a period of a couple-few months, the trend line has been set such that other periods will be below or above in turn. I want the differences to offset one another over time, and I try to ensure this is occurring each and every calendar year. This table is my way of checking how I’m doing. In this example, 2001 saw 307.5 billion shares sold; the estimate is at 306.4 billion, a difference of 1.1 billion, or 3/10 of 1%. Not bad, though again, the line that’s there is just a placeholder for the moment. Which explains why the differences in 2002 thru 2004 are much greater. Those will be addressed and reduced as we walk thru the trend estimation process.
  23. In the bottom right corner of the Estimating Trend section you will find a “Total” section that compares actuals and estimates for the entire time frame. In this instance it compares the totals for the entire 2001-16 period (in Column Q). These are all the years for which we have complete years of data; if the current year is a partial year, it should not be included in these totals. The total difference here should be very close to 0, and would hopefully have a total difference that is less than 1/10 of 1%, or certainly at most 1/10 of 1%. This helps ensure that while yearly differences may be fairly slight, that there is a tendency for the differences to offset over time, such that the total differences are truly tiny, on a percentage basis. Column R shows the year-to-date totals for the most current year. As we’ll see when we walk through updating the model for January 2017, this will be a place to compare the differences for the partial 2017 year.
  24. Occasionally, when you’re walking through the trend estimation process, you may find it helpful to have certain other time-related information at hand. Of particular note would be price changes, or marketing campaigns, or whatever. You could use this “Other Info” section as a place to have that info at hand as reference. I couldn’t think of anything worth tracking for the NYSE sales, so I’ve left it hidden. But I show it here so you’re aware it’s there, and think to put it to use for your own trending purposes.
  25. Now we turn to the Seasonal Factors Calculation section. In this section, we will start with the normalized data, then perform a series of calculations to adjust that data for the growth & events that have been input above. The exact formulas used here can be found in the Excel file attached to this website. We’ll quickly walk through each of the steps, and arrive ultimately at our final Growth-Adjusted Seasonal Factors.
  26. We start off the seasonal factor calculation by bringing in the normalized data. We work with the normalized data, not the actuals, because we want data that has been cleaned of the calendar effect, data where every month is of approximately equal length. Here we see September 2001 is quite bit higher than the other months. The actual sales for the month weren’t that high, but the exchange was open only 15 days that month, as it was closed for 9/11, and the following three days.
  27. We want to adjust for growth, so we begin by bringing in our estimates of the annual growth rate and events. The annual growth rate is divided by 12, in order to capture the impact of one month. The event estimate is picked up whole. Thus, for September 2001, we can see that 1/12th of the 2.0% annual rate has been picked up and combined with the 30% event figure. (Note that the formula is such that the amount here is slightly more than the sum of the two.)
  28. Next, we take our monthly growth rates (including events), and cumulate them, so we can properly get at how much higher (or lower) the year ends than it started. We also calculate the average growth rate for the year, which is the simple average of the 12 months of growth rates. The cumulative growth rate jumps in September 2001 as the prior month’s rate is increased by 30.2%.
  29. The cumulative growth rates are indexed, by adding 1 to each month’s cumulative rate and dividing it by 1 plus the average growth rate. September 2001’s index is (1+ 32%) divided by (1 + 4.6%). These indices capture the level of growth and events that is occurring across the year, and will be the factors used for adjusting the data for growth in the next step.
  30. The normalized data is adjusted for growth (& events) by dividing each month’s normalized sales by the Cumulative Growth Index. For September 2001, the normalized sales of 35.1 billion are divided by the 1.26 index to arrive at 27.8 billion. Note how this amount is now much closer to the other months’ amounts – the growth index has taken out the sales spike. Note also that a simple average figure has been calculated for each year – in Row 193.
  31. Now that we’ve adjusted the data for growth, we’re ready to zero in on determining the seasonal factors. We start by indexing the growth-adjusted data. September 2001’s growth-adjusted sales of 27.8 billion are divided by that year’s 26.3 billion average, to arrive at a factor of 1.06.
  32. We are now ready to determine the weighted average seasonal factors – we just need to know what years we wish to exclude as they contain a month(s) that is outside the acceptable range. As before, we achieve this by calculating a simple average & standard deviation for each month, then set an acceptable range based on the Maximum Permitted Standard Deviations. For September, the average across the 16 years happens to be 1.00, and the standard deviation is 0.10. we’ve set the maximum deviations at 2 (in Cell R199), so the bottom of the accepted range is the average (1.00) less 2 standard deviations (or 0.80) and the high end is the average plus 2 standard deviations (or 1.21). Looking across the years, we see only one occasion, 2008, where the factor falls outside the range; a conditional format highlights this outlier.
  33. Again, as we’ve seen before, a table is inserted that picks up whether or not each month falls within the accepted range. If it doesn’t, that month gets a “0”, and the year also gets a “0”, meaning it will not be included in the weighted average calculation.
  34. The last step in the calculation is to determine the weighted average for each month, using those years where every month met the acceptable range. Picking up the 8 accepted years for September, we arrive at a weighted average seasonal factor of 1.01.
  35. This may be redundant, but I wanted to remind you that these final factors are what are being picked up elsewhere in the model. These are the “Growth-Adjusted” seasonal factors displayed in the “Inputs” tab. And they are the “Final” factors picked up in the “Calc” tab.
  36. We’re now ready to move on to the 3rd and final key part of the “Trend” tab: the chart showing the seasonally-adjusted data, and our estimation of that data’s trend. Again, we’ll walk through this step-by-step.
  37. Absolutely central to estimating trend is the choice of the set of seasonal factors to employ. The choice is a manual input that you insert in the highlighted Cell AG1. As the note to the left indicates, a “1” means there is no seasonality, that all the factors are 1.00; a “2” picks up the Initial set of factors that we developed in the last chapter; and a “3” picks up the Final set of factors – this Final set is the growth-adjusted seasonal factors we are developing on this worksheet. And they are the same as we described on the last page, that are found near the foot of this “Trend” tab. A rule of thumb on which set of factors to employ: if you have nothing worth working with, use a “1” to assume no seasonality; if you do have something to work with, be it an initial set of factors you’ve developed, or a final set of factors you developed for some other set of data, use a “2” here. This initial set is what you work with while you walk through the FIRST iteration of your trend estimate. Once you’ve estimated trend, you should have an improved set of seasonal factors as they will have been adjusted for growth – accordingly, use a “3” to employ the Final growth-adjusted set.
  38. We now turn to the chart. The first thing to point out is that we want to initially have the chart focus on just a few years of the data. If we tried to estimate trend on 16 years of data at once, we’d have a difficult time seeing clearly how the data is behaving. To adjust the visible time range, you simply want to right-click on the X-axis, choose “Format axis”, and then set the “Minimum” and “Maximum” for the range of dates you want to focus on. Here we’ve focused on four years, 2001 through 2004. I also include Jan 2005 so that I can tell that ALL of 2004 is included.
  39. Similarly, you will want to set a Minimum and Maximum range for the Y-axis. Here the values are set such that you can see the top and bottom ends of the data you’re working with, for the time frame you’re working with.
  40. We’ll now go through the different lines depicted on the chart. First is the Actual data. Note that it is in very light gray. This is because we won’t really be using it very much; it’s here mainly as reference, as an FYI (for your information). But note that it is labeled “Actual (& Extrapolated) Values”. When we later look at forecasts, we’ll see that this line extends into the future, displaying what our forecast trend looks like after we’ve re-inserted the calendar effect and seasonality.
  41. The next line on the chart is the seasonally-adjusted data. It’s shown here in dotted blue. You can see that the line is certainly somewhat smoother than the original actuals. This line depicts the normalized data that has been seasonally-adjusted using the seasonal factors we chose at the top of the “Trend” tab.
  42. Recall that in the “Calc” tab we added a 3-month moving average for the seasonally-adjusted data. This was a way to help smooth the data and make it somewhat easier to read its behavior. That data is added here in the form of a thick solid blue line. I’ve emphasized this line because it is the one most used for observing how the data is trending. Why not just eliminate the dotted monthly seasonally-adjusted line? Because we’ll find the monthly is needed to better pinpoint the timing of when shifts occur in the data.
  43. The final line to add to the chart is our Estimated Trend line. This will be the key line, showing our estimates of how the data behaves over time, based on our inputs of growth rate & events. The line is in red, to help it stand out more. Note again that it is labeled the “Estimated (& Extrapolated) Trend” line. We’ll see it stretch out into the future when we get to the far end of the chart.
  44. That’s it for walking through how this model is structured. We saw the “Inputs” where we brought in our monthly data and normalization factors. We saw the “Calc” tab where most of the calculations are performed, and we’ve now seen how the “Trend” tab works. Going forward, our focus will be working with the top of this page, where in one view we are able to see our estimates of the growth rates & events, how our estimates compare with the actuals, the set of seasonal factors we’re using, and a chart displaying the key info we wish to track. This page shows the entire 2001-17 time period; when we start estimating the trend, we’ll hide the later years so as to better focus on those years being trended.
  45. Now we
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