Forecasting
Eight Steps to Forecasting

Determine the use of the forecast



Select the items or quantities that are to be forecasted.
Determine the time horizon of the forecast.








What objective are we trying to obtain?
Short time horizon – 1 to 30 days
Medium time horizon – 1 to 12 months
Long time horizon – more than 1 year
Select the forecasting model or models
Gather the data to make the forecast.
Validate the forecasting model
Make the forecast
Implement the results
Forecasting Models
Forecasting
Techniques
Qualitative
Models
Time Series
Methods
Delphi
Method
Jury of Executive
Opinion
Sales Force
Composite
Consumer Market
Survey
Naive
Moving
Average
Weighted
Moving Average
Exponential
Smoothing
Trend Analysis
Causal
Methods
Simple
Regression
Analysis
Multiple
Regression
Analysis
Seasonality
Analysis
Multiplicative
Decomposition
Model Differences
Qualitative – incorporates judgmental &
subjective factors into forecast.
 Time-Series – attempts to predict the
future by using historical data.
 Causal – incorporates factors that may
influence the quantity being forecasted
into the model

Qualitative Forecasting Models

Delphi method
 Iterative
group process allows experts to make
forecasts
 Participants:



decision makers: 5 -10 experts who make the forecast
staff personnel: assist by preparing, distributing, collecting,
and summarizing a series of questionnaires and survey
results
respondents: group with valued judgments who provide input
to decision makers
Qualitative Forecasting Models (cont)

Jury of executive opinion



Sales force composite




Opinions of a small group of high level managers, often in
combination with statistical models.
Result is a group estimate.
Each salesperson estimates sales in his region.
Forecasts are reviewed to ensure realistic.
Combined at higher levels to reach an overall forecast.
Consumer market survey.


Solicits input from customers and potential customers regarding
future purchases.
Used for forecasts and product design & planning
Forecast Error






Forecast Error  At  Ft
T
Bias - The arithmetic sum of
2
MSE

|
forecast
error
|
/T

the errors
t 1
Mean Square Error - Similar to
T
simple sample variance
  (At  Ft ) 2 / T
Variance - Sample variance
t 1
(adjusted for degrees of
freedom)
Standard Error - Standard
deviation of the sampling
distribution
T
T
MAD - Mean Absolute
MAD   | forecast error | /T   |At  Ft | / T
Deviation
t 1
t 1
MAPE – Mean Absolute
T
Percentage Error
MAPE  100 [|At  Ft | / At ] / T
t 1
Quantitative Forecasting Models

Time Series Method
 Naïve
 Whatever happened
recently will happen
again this time (same
time period)
 The model is simple
and flexible
 Provides a baseline to
measure other models
 Attempts to capture
seasonal factors at the
expense of ignoring
trend
Ft  Yt 1
Ft  Yt  4 : Quarterly data
Ft  Yt 12 : Monthly data
Naïve Forecast
Wallace Garden Supply
Forecasting
Period
January
February
March
April
May
June
July
August
September
October
November
December
Storage Shed Sales
Actual
Naïve
Value
Forecast
10
N/A
12
10
16
12
13
16
17
13
19
17
15
19
20
15
22
20
19
22
21
19
19
21
Error
2
4
-3
4
2
-4
5
2
-3
2
-2
9.000
BIAS
Absolute
Error
2
4
3
4
2
4
5
2
3
2
2
3
MAD
Percent
Error
16.67%
25.00%
23.08%
23.53%
10.53%
26.67%
25.00%
9.09%
15.79%
9.52%
10.53%
17.76%
MAPE
Standard Error (Square Root of MSE) =
Squared
Error
4.0
16.0
9.0
16.0
4.0
16.0
25.0
4.0
9.0
4.0
4.0
10.091
MSE
3.176619
Naïve Forecast Graph
Wallace Garden - Naive Forecast
25
20
Sheds
15
Actual Value
Naïve Forecast
10
5
0
February
March
April
May
June
July
Period
August
September
October
November
December
Quantitative Forecasting Models

Time Series Method
 Moving


Averages
Assumes item
forecasted will stay
steady over time.
Technique will smooth
out short-term
irregularities in the time
series.
k
k - period moving average   (Actual value in previous k periods) /k
k 1
Moving Averages
Wallace Garden Supply
Forecasting
Storage Shed Sales
Period
January
February
March
April
May
June
July
August
September
October
November
December
Actual
Value
10
12
16
13
17
19
15
20
22
19
21
19
Three-Month Moving Averages
10
12
16
13
17
19
15
20
22
+
+
+
+
+
+
+
+
+
12
16
13
17
19
15
20
22
19
+
+
+
+
+
+
+
+
+
16
13
17
19
15
20
22
19
21
/
/
/
/
/
/
/
/
/
3
3
3
3
3
3
3
3
3
=
=
=
=
=
=
=
=
=
12.67
13.67
15.33
16.33
17.00
18.00
19.00
20.33
20.67
Moving Averages Forecast
Wallace Garden Supply
Forecasting
3 period moving average
Input Data
Period
Month 1
Month 2
Month 3
Month 4
Month 5
Month 6
Month 7
Month 8
Month 9
Month 10
Month 11
Month 12
Next period
Actual Value - Forecast
Forecast Error Analysis
Actual Value
10
12
16
13
17
19
15
20
22
19
21
19
19.667
Forecast
12.667
13.667
15.333
16.333
17.000
18.000
19.000
20.333
20.667
Average
Error
0.333
3.333
3.667
-1.333
3.000
4.000
0.000
0.667
-1.667
12.000
BIAS
Absolute
error
0.333
3.333
3.667
1.333
3.000
4.000
0.000
0.667
1.667
2.000
MAD
Squared
error
0.111
11.111
13.444
1.778
9.000
16.000
0.000
0.444
2.778
6.074
MSE
Absolute
% error
2.56%
19.61%
19.30%
8.89%
15.00%
18.18%
0.00%
3.17%
8.77%
10.61%
MAPE
Moving Averages Graph
Three Period Moving Average
25
20
Value
15
Actual Value
Forecast
10
5
0
1
2
3
4
5
6
7
Time
8
9
10
11
12
Quantitative Forecasting Models

Time Series Method
 Weighted


Moving Averages
Assumes data from some periods are more
important than data from other periods (e.g.
earlier periods).
Use weights to place more emphasis on some
periods and less on others.
k - period weighted moving average 
k
k
i 1
i 1
 (Weight for each period i)(Actual value in previous k periods) /  (weights)
Weighted Moving Average
Wallace Garden Supply
Forecasting
Storage Shed Sales
Period
January
February
March
April
May
June
July
August
September
October
November
December
Next period
Actual
Value
Weights
10
0.222
12
0.593
16
0.185
13
17
19
15
20
22
19
21
19
20.185
Sum of weights =
1.000
Three-Month Weighted Moving Averages
2.2
2.7
3.5
2.9
3.8
4.2
3.3
4.4
4.9
+
+
+
+
+
+
+
+
+
7.1
9.5
7.7
10
11
8.9
12
13
11
+
+
+
+
+
+
+
+
+
3
2.4
3.2
3.5
2.8
3.7
4.1
3.5
3.9
/
/
/
/
/
/
/
/
/
1
1
1
1
1
1
1
1
1
=
=
=
=
=
=
=
=
=
12.298
14.556
14.407
16.484
17.814
16.815
19.262
21.000
20.036
Weighted Moving Average
Wallace Garden Supply
Forecasting
3 period weighted moving average
Input Data
Period
January
February
March
April
May
June
July
August
September
October
November
December
Next period
Sum of weights =
Forecast Error Analysis
Actual value
10
12
16
13
17
19
15
20
22
19
21
19
Weights
0.222
0.593
0.185
Forecast
12.298
14.556
14.407
16.484
17.814
16.815
19.262
21.000
20.036
Average
20.185
1.000
Error
0.702
2.444
4.593
-1.484
2.186
5.185
-0.262
0.000
-1.036
12.326
BIAS
Absolute
error
0.702
2.444
4.593
1.484
2.186
5.185
0.262
0.000
1.036
1.988
MAD
Squared Absolute %
error
error
0.492
5.971
21.093
2.202
4.776
26.889
0.069
0.000
1.074
6.952
MSE
5.40%
14.37%
24.17%
9.89%
10.93%
23.57%
1.38%
0.00%
5.45%
10.57%
MAPE
Quantitative Forecasting Models

Time Series Method
 Exponential
Smoothing
Moving average technique that requires little
record keeping of past data.
 Uses a smoothing constant α with a value between
0 and 1. (Usual range 0.1 to 0.3)

Forecast for period t 
forecast for period t - 1   (actual value in period t - 1 - forecast for period t - 1)
Exponential Smoothing Data
Storage Shed Sales
Exponential Smoothing
Period
January
February
March
April
May
June
July
August
September
October
November
December
Actual
Value
10
12
16
13
17
19
15
20
22
19
21
19
Ft
10
10
10
10
11
11
12
12
13
13
14
15
+
+
+
+
+
+
+
+
+
+
+
α
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
At
*(
*(
*(
*(
*(
*(
*(
*(
*(
*(
*(
10
12
16
13
17
19
15
20
22
19
21
Ft
-
10
10
10
11
11
12
12
13
13
14
15
Ft+1
)
)
)
)
)
)
)
)
)
)
)
=
=
=
=
=
=
=
=
=
=
=
10.000
10.200
10.780
11.002
11.602
12.342
12.607
13.347
14.212
14.691
15.322
Exponential Smoothing
Forecasting
Exponential smoothing
Input Data
Forecast Error Analysis
Period
Month 1
Month 2
Month 3
Month 4
Month 5
Month 6
Month 7
Month 8
Month 9
Month 10
Month 11
Month 12
Actual value
10
12
16
13
17
19
15
20
22
19
21
19
Alpha
0.100
Next period
15.690
Forecast
10.000
10.000
10.200
10.780
11.002
11.602
12.342
12.607
13.347
14.212
14.691
15.322
Average
Error
2.000
5.800
2.220
5.998
7.398
2.658
7.393
8.653
4.788
6.309
3.678
Absolute
error
2.000
5.800
2.220
5.998
7.398
2.658
7.393
8.653
4.788
6.309
3.678
5.172
MAD
Squared
error
4.000
33.640
4.928
35.976
54.733
7.067
54.650
74.879
22.925
39.806
13.529
31.467
MSE
Absolute
% error
16.67%
36.25%
17.08%
35.28%
38.94%
17.72%
36.96%
39.33%
25.20%
30.04%
19.36%
28%
MAPE
h
D
N
ct
ob
er
ec
em
be
r
ov
em
be
r
O
Se
pt
em
be
r
Au
gu
st
Ju
ly
Ju
ne
M
ay
Ap
ri l
M
ar
c
Fe
br
ua
ry
Ja
nu
ar
y
Sheds
Exponential Smoothing
Exponential Smoothing
25
20
15
Actual value
Forecast
10
5
0
Trend & Seasonality

Trend analysis



technique that fits a trend equation (or curve) to a series of
historical data points.
projects the curve into the future for medium and long term
forecasts.
Seasonality analysis



adjustment to time series data due to variations at certain
periods.
adjust with seasonal index – ratio of average value of the item in
a season to the overall annual average value.
example: demand for coal & fuel oil in winter months.
Linear Trend Analysis
Midwestern Manufacturing Sales
Sales(in units) vs. Time
Scatter Diagram
160
Actual
value (or)
Y
74
79
80
90
105
142
122
140
Period
number
(or) X
1995
1996
1997
1998
1999
2000
2001
120
100
Period number (or) X
80
60
40
20
0
1994
1996
1998
2000
2002
Least Squares for Linear Regression
Midwestern Manufacturing
Values of Dependent Variables
Least Squares Method
Time
Least Squares Method
^
Y  a  bX
Where
^
Y
= predicted value of the dependent variable (demand)
X = value of the independent
variable (time)
_ _
a = Y-axis intercept
b = slope of the regression line
b=
[ XY - n X Y ]
_

2
2
X
n
X




Linear Trend Data & Error Analysis
Midwestern Manufacturing Company
Forecasting
Linear trend analysis
Enter the actual values in cells shaded YELLOW. Enter new time period at the bottom to forecast
Input Data
Period
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Intercept
Slope
Next period
Forecast Error Analysis
Actual value Period number
(or) Y
(or) X
74
1
79
2
80
3
90
4
105
5
142
6
122
7
56.714
10.536
141.000
8
Forecast
67.250
77.786
88.321
98.857
109.393
119.929
130.464
Average
Error
6.750
1.214
-8.321
-8.857
-4.393
22.071
-8.464
Absolute
Squared Absolute
error
error
% error
6.750
45.563
9.12%
1.214
1.474
1.54%
8.321
69.246 10.40%
8.857
78.449
9.84%
4.393
19.297
4.18%
22.071 487.148 15.54%
8.464
71.644
6.94%
8.582 110.403
8.22%
MAD
MSE
MAPE
Least Squares Graph
Trend Analysis
160
140
y = 10.536x + 56.714
120
Value
100
80
60
40
20
0
1
2
3
4
5
Time
Actual values
Linear (Actual values)
6
7
Seasonality Analysis
Seasonal Index – ratio of the
average value of the item in a
Ratio = demand26/ average
demand season to the overall average
88.67 104.185
27
94.89 104.939 annual value.
February
March
April
May
June
July
August
September
October
November
December
January
February
March
April
May
June
July
August
September
October
November
December
28
29
30
31
32
33
34
35
36
112.44
139.29
131.15
120.59
115.65
104.81
93.80
94.45
95.09
105.693
106.448
107.202
107.957
108.711
109.465
110.220
110.974
111.729
Example: average of year 1
January ratio to year 2 Janua
ratio.
(0.851 + 1.064)/2 = 0.957
0.23265
slope
intercept
0.75441
84.5698
If the forecast for January of year 3 is
103, then
Forecast demand Year 3 January:
103 X 0.957 = 99 units
Forecast demand Year 3 May:
106 X 1.309 = 139 units
Название диаграммы
160
140
120
100
80
60
40
20
0
0
5
10
15
20
Ряд1
25
Ряд2
30
35
40
Seasonality Analysis
Ratio = demand / average demand
Eichler Supplies
Year
1
2
Month
January
February
March
April
May
June
July
August
September
October
November
December
January
February
March
April
May
June
July
August
September
October
November
December
Average
Demand Demand
80
94
75
94
80
94
90
94
115
94
110
94
100
94
90
94
85
94
75
94
75
94
80
94
100
94
85
94
90
94
110
94
131
94
120
94
110
94
110
94
95
94
85
94
85
94
80
94
Ratio
0.851
0.798
0.851
0.957
1.223
1.170
1.064
0.957
0.904
0.798
0.798
0.851
1.064
0.904
0.957
1.170
1.394
1.277
1.170
1.170
1.011
0.904
0.904
0.851
Seasonal
Index
0.957
0.851
0.904
1.064
1.309
1.223
1.117
1.064
0.957
0.851
0.851
0.851
83.55556
88.125
88.47059
84.6
87.88618
89.91304
89.52381
84.6
88.77778
88.125
88.125
94
104.4444
1
2
3
4
5
6
7
8
9
10
11
12
13
Seasonal Index – ratio of the
average value of the item in a
season to the overall average
annual value.
Example: average of year 1
January ratio to year 2 January
ratio.
(0.851 + 1.064)/2 = 0.957
If the forecast for January of year 3 is
103, then
Forecast demand Year 3 January:
103 X 0.957 = 99 units
Forecast demand Year 3 May:
106 X 1.309 = 139 units
130.861
Seasonality Analysis
Ratio = demand / average demand
Eichler Supplies
Average
Demand Demand
Month
Year
94
80
January
1
94
75
February
94
80
March
94
90
April
94
115
May
94
110
June
94
100
July
94
90
August
94
85
September
94
75
October
94
75
November
94
80
December
94
100
January
2
94
85
February
94
90
March
94
110
April
94
131
May
94
120
June
94
110
July
94
110
August
94
95
September
94
85
October
94
85
November
94
80
December
Ratio
0.851
Seasonal
Index
0.851
94
1
Seasonal
Index – ratio of the
average value of the item in a
season to the overall average
annual value.
Example: average of year 1
January ratio to year 2 January
ratio.
(0.851 + 1.064)/2 = 0.957
If the forecast for January of year 3 is
103, then
Forecast demand Year 3 January:
103 X 0.957 = 99 units
Forecast demand Year 3 May:
106 X 1.309 = 139 units
130.861
Deseasonalized Data

Going back to the conceptual model, solve
for trend:

Trend = Y / Season
(96 units/ 0.957 = 100.31)
This eliminates seasonal variation and
isolates the trend
 Now use the Least Squares method to
compute the Trend

Forecast

Now that we have the Seasonal Indices
and Trend, we can reseasonalize the data
and generate the forecast

Y = Trend x Seasonal Index
Causal Method
Y = a + bX as in the least square methods
 Y = the dependent variable
 X = the independent variable

Coefficient of correlation
Causal
student population
1,234
1,256
1,345
1,678
2,145
2,345
2,357
correlation
coefficient
slope =
intercept =
juice (in glasses)
X
Y
6,042
5,430
6,345
5,671
6,251
6,891
6,789
0.746112
0.790213
4807.424
Multiple regression