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Demand Forecasting:
Time Series Models
Professor Stephen R. Lawrence
College of Business and Administration
University of ...
Forecasting Horizons
Long Term
• 5+ years into the future
• R&D, plant location, product planning
• Principally judgement-...
Short Term Forecasting:
Needs and Uses
Scheduling existing resources
• How many employees do we need and when?
• How much ...
Types of Forecasting Models
Types of Forecasts
• Qualitative --- based on experience, judgement, knowledge;
• Quantitative...
Forecasting Examples
Examples from student projects:
• Demand for tellers in a bank;
• Traffic on major communication swit...
Simple Moving Average
Forecast Ft is average of n previous observations or
actuals Dt:
Note that the n past observations a...
Simple Moving Average
Include n most recent observations
Weight equally
Ignore older observations
weight
today
123...n
1/n...
Moving Average
Internet Unicycle Sales
0
50
100
150
200
250
300
350
400
450
Apr-01 Sep-02 Jan-04 May-05 Oct-06 Feb-08 Jul-...
Example:
Moving Average
Forecasting
http://ebooks.edhole.com
Exponential Smoothing I
Include all past observations
Weight recent observations much more heavily
than very old observati...
Exponential Smoothing I
Include all past observations
Weight recent observations much more heavily
than very old observati...
Exponential Smoothing I
Include all past observations
Weight recent observations much more heavily
than very old observati...
Exponential Smoothing I
Include all past observations
Weight recent observations much more heavily
than very old observati...
Exponential Smoothing: Concept
Include all past observations
Weight recent observations much more heavily
than very old ob...
Exponential Smoothing: Math
[ ]

+−+−+=
+−+−+=
−−
−−
21
2
2
1
)1()1(
)1()1(
tttt
tttt
DaDDF
DDDF
αααα
ααααα
http://ebook...
Exponential Smoothing: Math
1)1( −−+= ttt FaaDF
[ ]

+−+−+=
+−+−+=
−−
−−
21
2
2
1
)1()1(
)1()1(
tttt
tttt
DaDDF
DDDF
ααα...
Exponential Smoothing: Math
Thus, new forecast is weighted sum of old forecast and actual
demand
Notes:
• Only 2 values (D...
Exponential Smoothing
Internet Unicycle Sales (1000's)
0
50
100
150
200
250
300
350
400
450
Jan-03 May-04 Sep-05 Feb-07 Ju...
Example:
Exponential Smoothing
http://ebooks.edhole.com
Complicating Factors
Simple Exponential Smoothing works well
with data that is “moving sideways”
(stationary)
Must be adap...
Holt’s Method:
Double Exponential Smoothing
What happens when there is a definite trend?
A trendy clothing boutique has ha...
Holt’s Method:
Double Exponential Smoothing
Ideas behind smoothing with trend:
• ``De-trend'' time-series by separating ba...
ES with Trend
Internet Unicycle Sales (1000's)
0
50
100
150
200
250
300
350
400
450
Jan-03 May-04 Sep-05 Feb-07 Jun-08 Nov...
Example:
Exponential Smoothing
with Trend
http://ebooks.edhole.com
Winter’s Method:
Exponential Smoothing
w/ Trend and Seasonality
Ideas behind smoothing with trend and seasonality:
• “De-t...
Winter’s Method:
Exponential Smoothing
w/ Trend and Seasonality
Smooth the base forecast Bt
Smooth the trend forecast Tt
S...
Winter’s Method:
Exponential Smoothing
w/ Trend and Seasonality
Forecast Ft with trend and seasonality
Smooth the trend fo...
ES with Trend and Seasonality
Internet Unicycle Sales (1000's)
0
50
100
150
200
250
300
350
400
450
500
Jan-03 May-04 Sep-...
Example:
Exponential Smoothing
with
Trend and Seasonality
http://ebooks.edhole.com
Forecasting Performance
Mean Forecast Error (MFE or Bias): Measures
average deviation of forecast from actuals.
Mean Absol...
Forecasting Performance Measures
)(
1
1
t
n
t
t FD
n
MFE −= ∑=
∑=
−=
n
t
tt FD
n
MAD
1
1
∑=
−
=
n
t t
tt
D
FD
n
MAPE
1
100...
Want MFE to be as close to zero as possible --
minimum bias
A large positive (negative) MFE means that the
forecast is und...
Mean Absolute Deviation (MAD)
Measures absolute error
Positive and negative errors thus do not cancel out (as
with MFE)
Wa...
Mean Absolute Percentage Error
(MAPE)
Same as MAD, except ...
Measures deviation as a percentage of actual data
∑=
−
=
n
t...
Mean Squared Error (MSE)
Measures squared forecast error -- error variance
Recognizes that large errors are disproportiona...
Fortunately, there is software...
http://ebooks.edhole.com
Free Ebooks Download
Mba Ebooks
By Edhole
Mba ebooks
Free ebooks download
http://ebooks.edhole.com
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  • Free ebooks download ! Edhole

    1. 1. Free Ebooks Download Mba Ebooks By Edhole Mba ebooks Free ebooks download http://ebooks.edhole.com
    2. 2. Demand Forecasting: Time Series Models Professor Stephen R. Lawrence College of Business and Administration University of Colorado Boulder, CO 80309-0419 http://ebooks.edhole.com
    3. 3. Forecasting Horizons Long Term • 5+ years into the future • R&D, plant location, product planning • Principally judgement-based Medium Term • 1 season to 2 years • Aggregate planning, capacity planning, sales forecasts • Mixture of quantitative methods and judgement Short Term • 1 day to 1 year, less than 1 season • Demand forecasting, staffing levels, purchasing, inventory levels • Quantitative methods http://ebooks.edhole.com
    4. 4. Short Term Forecasting: Needs and Uses Scheduling existing resources • How many employees do we need and when? • How much product should we make in anticipation of demand? Acquiring additional resources • When are we going to run out of capacity? • How many more people will we need? • How large will our back-orders be? Determining what resources are needed • What kind of machines will we require? • Which services are growing in demand? declining? • What kind of people should we be hiring? http://ebooks.edhole.com
    5. 5. Types of Forecasting Models Types of Forecasts • Qualitative --- based on experience, judgement, knowledge; • Quantitative --- based on data, statistics; Methods of Forecasting • Naive Methods --- eye-balling the numbers; • Formal Methods --- systematically reduce forecasting errors; – time series models (e.g. exponential smoothing); – causal models (e.g. regression). • Focus here on Time Series Models Assumptions of Time Series Models • There is information about the past; • This information can be quantified in the form of data; • The pattern of the past will continue into the future. http://ebooks.edhole.com
    6. 6. Forecasting Examples Examples from student projects: • Demand for tellers in a bank; • Traffic on major communication switch; • Demand for liquor in bar; • Demand for frozen foods in local grocery warehouse. Example from Industry: American Hospital Supply Corp. • 70,000 items; • 25 stocking locations; • Store 3 years of data (63 million data points); • Update forecasts monthly; • 21 million forecast updates per year. http://ebooks.edhole.com
    7. 7. Simple Moving Average Forecast Ft is average of n previous observations or actuals Dt: Note that the n past observations are equally weighted. Issues with moving average forecasts: • All n past observations treated equally; • Observations older than n are not included at all; • Requires that n past observations be retained; • Problem when 1000's of items are being forecast. ∑−+= + −+−+ = +++= t nti it ntttt D n F DDD n F 1 1 111 1 )( 1  http://ebooks.edhole.com
    8. 8. Simple Moving Average Include n most recent observations Weight equally Ignore older observations weight today 123...n 1/n http://ebooks.edhole.com
    9. 9. Moving Average Internet Unicycle Sales 0 50 100 150 200 250 300 350 400 450 Apr-01 Sep-02 Jan-04 May-05 Oct-06 Feb-08 Jul-09 Nov-10 Apr-12 Aug-13 Month Units n = 3 http://ebooks.edhole.com
    10. 10. Example: Moving Average Forecasting http://ebooks.edhole.com
    11. 11. Exponential Smoothing I Include all past observations Weight recent observations much more heavily than very old observations: weight today Decreasing weight given to older observations http://ebooks.edhole.com
    12. 12. Exponential Smoothing I Include all past observations Weight recent observations much more heavily than very old observations: weight today Decreasing weight given to older observations 0 1< <α α http://ebooks.edhole.com
    13. 13. Exponential Smoothing I Include all past observations Weight recent observations much more heavily than very old observations: weight today Decreasing weight given to older observations 0 1< <α α α α( )1− http://ebooks.edhole.com
    14. 14. Exponential Smoothing I Include all past observations Weight recent observations much more heavily than very old observations: weight today Decreasing weight given to older observations 0 1< <α α α α α α ( ) ( ) 1 1 2 − − http://ebooks.edhole.com
    15. 15. Exponential Smoothing: Concept Include all past observations Weight recent observations much more heavily than very old observations: weight today Decreasing weight given to older observations 0 1< <α α α α α α α α ( ) ( ) ( ) 1 1 1 2 3 − − −  http://ebooks.edhole.com
    16. 16. Exponential Smoothing: Math [ ]  +−+−+= +−+−+= −− −− 21 2 2 1 )1()1( )1()1( tttt tttt DaDDF DDDF αααα ααααα http://ebooks.edhole.com
    17. 17. Exponential Smoothing: Math 1)1( −−+= ttt FaaDF [ ]  +−+−+= +−+−+= −− −− 21 2 2 1 )1()1( )1()1( tttt tttt DaDDF DDDF αααα ααααα http://ebooks.edhole.com
    18. 18. Exponential Smoothing: Math Thus, new forecast is weighted sum of old forecast and actual demand Notes: • Only 2 values (Dt and Ft-1 ) are required, compared with n for moving average • Parameter a determined empirically (whatever works best) • Rule of thumb: α < 0.5 • Typically, α = 0.2 or α = 0.3 work well Forecast for k periods into future is: 1 2 2 1 )1( )1()1( − −− −+= +−+−+= ttt tttt FaaDF DaaDaaaDF  tkt FF =+ http://ebooks.edhole.com
    19. 19. Exponential Smoothing Internet Unicycle Sales (1000's) 0 50 100 150 200 250 300 350 400 450 Jan-03 May-04 Sep-05 Feb-07 Jun-08 Nov-09 Mar-11 Aug-12 Month Units α = 0.2 http://ebooks.edhole.com
    20. 20. Example: Exponential Smoothing http://ebooks.edhole.com
    21. 21. Complicating Factors Simple Exponential Smoothing works well with data that is “moving sideways” (stationary) Must be adapted for data series which exhibit a definite trend Must be further adapted for data series which exhibit seasonal patterns http://ebooks.edhole.com
    22. 22. Holt’s Method: Double Exponential Smoothing What happens when there is a definite trend? A trendy clothing boutique has had the following sales over the past 6 months: 1 2 3 4 5 6 510 512 528 530 542 552 480 490 500 510 520 530 540 550 560 1 2 3 4 5 6 7 8 9 10 Month Demand Actual Forecast http://ebooks.edhole.com
    23. 23. Holt’s Method: Double Exponential Smoothing Ideas behind smoothing with trend: • ``De-trend'' time-series by separating base from trend effects • Smooth base in usual manner using α • Smooth trend forecasts in usual manner using β Smooth the base forecast Bt Smooth the trend forecast Tt Forecast k periods into future Ft+k with base and trend ))(1( 11 −− +−+= tttt TBDB αα 11 )1()( −− −+−= tttt TBBT ββ ttkt kTBF +=+ http://ebooks.edhole.com
    24. 24. ES with Trend Internet Unicycle Sales (1000's) 0 50 100 150 200 250 300 350 400 450 Jan-03 May-04 Sep-05 Feb-07 Jun-08 Nov-09 Mar-11 Aug-12 Month Units α = 0.2, β = 0.4 http://ebooks.edhole.com
    25. 25. Example: Exponential Smoothing with Trend http://ebooks.edhole.com
    26. 26. Winter’s Method: Exponential Smoothing w/ Trend and Seasonality Ideas behind smoothing with trend and seasonality: • “De-trend’: and “de-seasonalize”time-series by separating base from trend and seasonality effects • Smooth base in usual manner using α • Smooth trend forecasts in usual manner using β • Smooth seasonality forecasts using γ Assume m seasons in a cycle • 12 months in a year • 4 quarters in a month • 3 months in a quarter • et cetera http://ebooks.edhole.com
    27. 27. Winter’s Method: Exponential Smoothing w/ Trend and Seasonality Smooth the base forecast Bt Smooth the trend forecast Tt Smooth the seasonality forecast St ))(1( 11 −− − +−+= tt mt t t TB S D B αα 11 )1()( −− −+−= tttt TBBT ββ mt t t t S B D S −−+= )1( γγ http://ebooks.edhole.com
    28. 28. Winter’s Method: Exponential Smoothing w/ Trend and Seasonality Forecast Ft with trend and seasonality Smooth the trend forecast Tt Smooth the seasonality forecast St mktttkt SkTBF −+−−+ += )( 11 11 )1()( −− −+−= tttt TBBT ββ mt t t t S B D S −−+= )1( γγ http://ebooks.edhole.com
    29. 29. ES with Trend and Seasonality Internet Unicycle Sales (1000's) 0 50 100 150 200 250 300 350 400 450 500 Jan-03 May-04 Sep-05 Feb-07 Jun-08 Nov-09 Mar-11 Aug-12 Month Units α = 0.2, β = 0.4, γ = 0.6 http://ebooks.edhole.com
    30. 30. Example: Exponential Smoothing with Trend and Seasonality http://ebooks.edhole.com
    31. 31. Forecasting Performance Mean Forecast Error (MFE or Bias): Measures average deviation of forecast from actuals. Mean Absolute Deviation (MAD): Measures average absolute deviation of forecast from actuals. Mean Absolute Percentage Error (MAPE): Measures absolute error as a percentage of the forecast. Standard Squared Error (MSE): Measures variance of forecast error How good is the forecast? http://ebooks.edhole.com
    32. 32. Forecasting Performance Measures )( 1 1 t n t t FD n MFE −= ∑= ∑= −= n t tt FD n MAD 1 1 ∑= − = n t t tt D FD n MAPE 1 100 2 1 )( 1 t n t t FD n MSE −= ∑= http://ebooks.edhole.com
    33. 33. Want MFE to be as close to zero as possible -- minimum bias A large positive (negative) MFE means that the forecast is undershooting (overshooting) the actual observations Note that zero MFE does not imply that forecasts are perfect (no error) -- only that mean is “on target” Also called forecast BIAS Mean Forecast Error (MFE or Bias) )( 1 1 t n t t FD n MFE −= ∑= http://ebooks.edhole.com
    34. 34. Mean Absolute Deviation (MAD) Measures absolute error Positive and negative errors thus do not cancel out (as with MFE) Want MAD to be as small as possible No way to know if MAD error is large or small in relation to the actual data ∑= −= n t tt FD n MAD 1 1 http://ebooks.edhole.com
    35. 35. Mean Absolute Percentage Error (MAPE) Same as MAD, except ... Measures deviation as a percentage of actual data ∑= − = n t t tt D FD n MAPE 1 100 http://ebooks.edhole.com
    36. 36. Mean Squared Error (MSE) Measures squared forecast error -- error variance Recognizes that large errors are disproportionately more “expensive” than small errors But is not as easily interpreted as MAD, MAPE -- not as intuitive 2 1 )( 1 t n t t FD n MSE −= ∑= http://ebooks.edhole.com
    37. 37. Fortunately, there is software... http://ebooks.edhole.com
    38. 38. Free Ebooks Download Mba Ebooks By Edhole Mba ebooks Free ebooks download http://ebooks.edhole.com

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