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Forecasting
} I. DEFINITION OF FORECASTING
} II. IMPORTANCE OF FORECASTING
} III. CHOICE OF FORECASTING SYSTEMS
} IV. MEASURES OF FORECAST ERRORS
} V.TYPES OF FORECASTING METHODS
} VI.COMPUTER DEMONSTRATION
I. DEFINITION OF FORECASTING
} The ability to predict the future, yields to better decision
making.
II. IMPORTANCE OF FORECASTING
} Governments http://www.youtube.com/watch?
v=kjy5Rvi3yx4
} Hurricanes/famine
} Companies find forecasting to be a useful tool in gaining a
competitive advantage.
} Jet fuel
} Individuals also find forecasts to be useful.
} Weather

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III. CHOICE OF FORECASTING SYSTEMS
} A. COSTVS ACCURACY
} To develop a forecasting system you need to decide
} The type of information needed,
} The aggregation level, and the
} Complexity of the forecasting model.
} Information technologies.
} Good forecasting system can be developed without much cost
¨ Easy data
¨ Cheap PC
III. CHOICE OF FORECASTING SYSTEMS
} B. DATA AVAILABILITY/SOURCE
} Think about all the sources of data.
} Today is a problem of getting the right data
} Sorting out from too much.
III. CHOICE OF FORECASTING SYSTEMS
} C. PERFORMANCE OF THE MODEL
} 1. RESPONSIVENESSV.S. STABILITY
} Responsiveness refers to how quickly a forecasting
model adapts to a underlying change in a process.
} Stability refers to its ability to overcome spikes and
natural variability.

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} A few useful terms:
} Accuracy -
} Precision -
} Bias -
IV. MEASURES OF FORECAST ERRORS

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A. STANDARD MEASURES
At Ft ei
|ei|
ei²
25 20
55 60
55 50
85 90
∑ ∑ ∑
ME MAD MSE
V. TYPES OF FORECASTING METHODS
Data Availability Causal Time series
Costly decisions
Time series
Routine Decisions
Large amount Linear Regression Box-Jenkins
Econometrics
Exponential smoothing
& moving averages
Little Delphi
Brainstorming
Delphi method
Market Surveys
Bayes methods
V. TYPES OF FORECASTING METHODS
} A. LITTLE OR NO FORECASTING
} Many operations still do not have forecasting systems in place
} B. QUALITATIVE (90% of the forecasts are qualitative)
} Historically, upper management has relied on qualitative methods.
} However, these methods lack the necessary precision and the
forecasts go usually undocumented.
} Examples:

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C. QUANTITATIVE
} 1. Explanatory: (causal)
} Tend to be of higher quality in that we map
out the relationships
} GNPt+1= f(monetary, fiscal, import..)
Input
Identify
Process
Output
} 2. Univariate (one variable over time)
} GNPt+1= f(GNPt, GNPt-1, GNPt-2, ...)
} To get identify the historical pattern we need to
dissect (decompose) the data into various
components and then smooth out the remnants
Input
Black box
Output
C. QUANTITATIVE
Day At Ft At-Ft |At-Ft| (At-Ft)2
1 60
2 65
3 80
4 70
5 73
6 80
7
Sum ∑ ∑ ∑
ME MAD MSE
TIME SERIES METHODS
a) simple moving average
In this model we employ a weighing function of n=3

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50
55
60
65
70
75
80
85
1 2 3 4 5 6
Temperature
Day
Raw Data
SMA
WMA
Plot SMA, WMA & EXP
Day At Ft At-Ft |At-Ft| (At-Ft)2
1 60
2 65
3 80
4 70
5 73
6 80
7
∑ ∑ ∑
ME MAD MSE
B) weighted moving average
In this model we employ a weighing function of n=3 (x1,x2,x3)
Day At Ft At-Ft |At-Ft| (At-Ft)2
1 60
2 65
3 80
4 70
5 73
6 80
7
∑ ∑ ∑
ME MAD MSE
Single exponential
Derive the equation below: Ft+1 = Ft + α(At-Ft) to Ft+1 = (1-α)Ft + α(At)
WEIGHING α =.2

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t-6 t-5 t-4 t-3 t-2 t-1 t
0
0.1
0.2
0.3
0.4
0.5
SMA (n=3) WMA (n=3) x1, x2, x3 SMA (n=2)
Weighing function
α Responsive? Lower forecast error Average age of data
High 0.9 more responsive with trend & process change in
the data
short
Low 0.1 more stable with normal fluctuations in the
data
long
0
0.2
0.4
0.6
0.8
1
t t-1 t-2 t-3
alpha =.5
alpha = .7
alpha = .9
D) TREND & SEASONALITY
The variable you are attempting to forecast might
display a trend or seasonality.

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2. Decomposition: Assuming you run an ice-cream parlor and
you want to track the sales by quarter
} Step 1. Plot the data
Quaters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
0
10
20
30
40
50
60
70
80
90
100
110
120
Raw
Ice Cream Demand
Step 2: Fit a trend line
Quaters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
Trend Raw
Ice Cream Demand
Compute residuals
Quaters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
Trend Raw
Ice Cream Demand
Quaters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
-20
-10
0
10
20
30
Raw-Trend
Ice Cream Demand

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Step 4. Now fit a cyclical pattern
Quaters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
-20
-10
0
10
20
30
Raw-Trend
Ice Cream Demand
Quaters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
-20
-10
0
10
20
30
Cyclical Raw-Trend
Ice Cream Demand
Step 5. Plot residuals from raw - trend - cyclical
Quaters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
-20
-10
0
10
20
30
Cyclical Raw-Trend
Ice Cream Demand
Quaters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
-20
-10
0
10
20
30
Raw-Trend-Cyclical
Step 6: Fit a seasonal pattern
Quaters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
-20
-10
0
10
20
30
Raw-Trend-Cyclical

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Step 7. Remaining residuals should be noise - simply
discard
Quaters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
-20
-10
0
10
20
30
Seasonal Raw-Trend-Cyclical
Quaters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
-20
-10
0
10
20
30
Noise=Raw-Trend-Cyclical-Seasonal
Decomposition
} Summary
} There are four components to a series:
} Trend (T)
} Seasonal (S)
} Non-annual cycle ( C)
} Random error (E)
} 2. Steps for decomposition
} Additive model
¨ RW - T - C - S = E
} Add back the components identified
therefore:
¨ F = T + C + S or F = T * C * S
Now forecast extend trend out.
Quaters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
Trend Raw
Ice Cream Demand

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Now forecast extent trend plus add
cyclical
Quaters
18 19 20 21 22 23 24
80
90
100
110
120
130
Trend Raw
Ice Cream Demand
Now extent forecast: trend plus add
cyclical and seasonal
Quaters
18 19 20 21 22 23 24
80
90
100
110
120
130
Trend Raw
Trend + cyclical Plus seasonal
Ice Cream Demand
Mini assignment
} Using the data for ice cream demand, compute the
seasonal indices.
} S- seasonal -
} 1) over that last few years sum the At (residuals if fitted by the
trend) for each month (or quarter) and divide by the number
of years.
} 2) obtain a mean value for all the months (or quarters) .
} 3) the seasonal index for each month (or quarter) is the ratio
of (1)/(2).

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2. EXPLANATORY (80%)
Months
1 2 3 4 5 6 7 8 9 10 11
0
20
40
60
80
100
120
140
Legend
Demand
Lagged by 3 months
WESFI
2. EXPLANATORY (80%)
Months
1 2 3 4 5 6 7 8 9 10 11
0
20
40
60
80
100
120
140
Legend
Permits
Demand
Lagged by 3 months
WESFI
2. EXPLANATORY (80%)
Months
1 2 3 4 5 6 7 8 9 10 11
0
20
40
60
80
100
120
140
Legend
Permits Demand
Forecast
Lagged by 3 months
WESFI

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Lagged regression
Y
X
a
b
Y = a + b x
Month Sales Million $/yr Permits
1 14.4 20
2 16.9 24
3 20.5 27
4 26.8 25
5 14.9 20
6 12 18
7 ?
Example Using Linear Regression
Given the following data, the company wants to estimate the sales in year 7.
Use linear regression to obtain the estimated sales and
compute the correlation coefficient (1,2 & 3 months lag).
X2 Y2 XY
∑ ∑ ∑ ∑ ∑
A) FILL IN THE TABLE BELOW

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Calculating estimates
∑ ∑
∑ ∑ ∑ ∑
−
−
= 22
2
)( xxn
xyxyx
a
∑ ∑
∑ ∑ ∑
−
−
= 22
)( xxn
yxxyn
b
∑∑∑ ∑
∑ ∑ ∑
−−
−
=
])()][)([ 2222
yynxxn
yxxyn
r
What r tells us
Wind speed
0 2 4 6 8 10
0
1
2
3
4
5
6
R close to zero
GPA
1 1.5 2 2.5 3 3.5 4
0
2
4
6
8
10
R close to +1
Hours party/day
0 2 4 6 8 10
0
1
2
3
4
5
6
7
R close to -1
Forecasting
} I. DEFINITION OF FORECASTING
} II. IMPORTANCE OF FORECASTING
} III. CHOICE OF FORECASTING SYSTEMS
} A. COSTVS ACCURACY
} B. DATA AVAILABILITY
} C. PERFORMANCE OF THE MODEL
} 1. RESPONSIVENESSVS STABILITY
} 2. FORECAST ERROR
} IV. MEASURES OF FORECAST ERRORS
} A. STANDARD MEASURES
} V.TYPES OF FORECASTING METHODS
} A. LITTLE OR NO FORECASTING
} B. QUALITATIVE
} C. QUANTITATIVE
} 1.TIME SERIES
} 2. EXPLANATORY/CAUSAL
} D.TREND & SEASONALITY
} VI.COMPUTER DEMONSTRATION