Deseasonalizing
Forecasts
Prepared by Aaron Hirst
Brigham Young University
Fall 2005
Agenda:
•
•
•
•
•
•
•
•
•
Seasonality defined & seasonal adjustment methods
Brainstorming Exercise
Nuts and Bolts
How It Works
Seasonal adjustment example
Exercise
Summary
Reading List
Appendix A: Solution to Exercise
Seasonality
• A repeated pattern of spikes or drops in the
variable of interest associated with a period
of time
• Examples– Consumer buying habits
– Price of gasoline
Seasonality
• Causes of seasonal movement by class:
1. Weather (temperature, precipitation)
2. Calendar Events (religious or secular
festivals)
3. Timing decisions (vacations, accounting
periods)
Seasonal Adjustment Methods
•
•
•
•
•
•
X-12 ARIMA
X-11 ARIMA
EEC Method
Burman Method
TRAMO
Seasonal index
Brainstorming Exercise
• How can this tool be used in your
organization?
Nuts and Bolts
Why make seasonal adjustments?
– Reduces errors in time-series forecasting
– Improves quality of judgmental forecasts
– Gives good insight into the factors influencing demand
The purpose of finding seasonal indexes is to remove
the seasonal effects from the time series
How It Works:
Deseasonalizing Forecasts
Four-step procedure for seasonal adjustments:
1. Calculate forecast for each demand values in the
time series
2. For each demand value, calculate
Demand/Forecast
3. Average the Demand/Forecast for months or
quarters to get the seasonal index
4. Multiply the unadjusted forecast by the seasonal
index to find adjusted forecast value
Season Adjustment Example
• Foster Company makes widgets. The
quarterly demand for its widget is
given in Exhibit 1
• Using linear regression forecasting,
develop a seasonal index for each
quarter and reforecast each quarter
Exhibit 1
Year Quarter Demand
1
1
72
2
110
3
117
4
172
2
1
76
2
112
3
130
4
194
3
1
78
2
119
3
128
4
201
4
1
81
2
134
3
141
4
216
Seasonal Adjustments Example
Step 1
Calculate forecast for each demand values
in the time series
– Use the unadjusted regression forecast model
Y= a + bx
Seasonal Adjustments Example – Step 1
Exhibit 2
• Forecasted demand
Y=95.85+4.03*period
• Year 1 Quarter 1:
Y=95.85+4.03(1)
=99.9
Unadjusted
Regression
Period Year Quarter Demand
Forecast
1
1
1
72
99.9
2
2
110
103.9
3
3
117
107.9
4
4
172
112.0
5
2
1
76
116.0
6
2
112
120.0
7
3
130
124.1
8
4
194
128.1
9
3
1
78
132.1
10
2
119
136.2
11
3
128
140.2
12
4
201
144.2
13
4
1
81
148.2
14
2
134
152.3
15
3
141
156.3
16
4
216
160.3
Seasonal Adjustments Example – Step 2
Exhibit 3
• For each demand
value, calculate
Demand/Forecast
• Year 1 Quarter 1:
72/99.9= 0.72
Unadjusted
Regression Demand/
Period Year Quarter Demand
Forecast Forecast
1
1
1
72
99.9
0.72
2
2
110
103.9
1.06
3
3
117
107.9
1.08
4
4
172
112.0
1.54
5
2
1
76
116.0
0.66
6
2
112
120.0
0.93
7
3
130
124.1
1.05
8
4
194
128.1
1.51
9
3
1
78
132.1
0.59
10
2
119
136.2
0.87
11
3
128
140.2
0.91
12
4
201
144.2
1.39
13
4
1
81
148.2
0.55
14
2
134
152.3
0.88
15
3
141
156.3
0.90
16
4
216
160.3
1.35
Seasonal Adjustments Example - Step 3
Exhibit 4
• Average the Demand/Forecast for
the quarters to get the seasonal
index
• Quarterly Seasonal Index for
Quarter 1:
(0.72+0.66+0.59+0.55)/4 = 0.63
Quarterly
Demand/ Seasonal
Period Year Quarter Forecast
Index
1
1
1
0.72
0.63
2
2
1.06
0.94
3
3
1.08
0.99
4
4
1.54
1.45
5
2
1
0.66
0.63
6
2
0.93
0.94
7
3
1.05
0.99
8
4
1.51
1.45
9
3
1
0.59
0.63
10
2
0.87
0.94
11
3
0.91
0.99
12
4
1.39
1.45
13
4
1
0.55
0.63
14
2
0.88
0.94
15
3
0.90
0.99
16
4
1.35
1.45
Seasonal Adjustments Example - Step 4
• Multiply the unadjusted forecast by the
seasonal index to find the adjusted forecast
values
• Year 1 Quarter 1:
99.9 * 0.63 = 62.7 (adjusted forecast)
Seasonal Adjustments Example - Step 4
Exhibit 5
Period Year Quarter Demand
1
1
1
72
2
2
110
3
3
117
4
4
172
5
2
1
76
6
2
112
7
3
130
8
4
194
9
3
1
78
10
2
119
11
3
128
12
4
201
13
4
1
81
14
2
134
15
3
141
16
4
216
Unadjusted
Regression Demand/
Forecast
Forecast
99.9
0.72
103.9
1.06
107.9
1.08
112.0
1.54
116.0
0.66
120.0
0.93
124.1
1.05
128.1
1.51
132.1
0.59
136.2
0.87
140.2
0.91
144.2
1.39
148.2
0.55
152.3
0.88
156.3
0.90
160.3
1.35
Quarterly
Seasonal
Index
0.63
0.94
0.99
1.45
0.63
0.94
0.99
1.45
0.63
0.94
0.99
1.45
0.63
0.94
0.99
1.45
Adjusted
Regression
Forecast
62.7
97.3
106.5
162.1
72.9
112.4
122.4
185.5
83.0
127.5
138.3
208.8
93.1
142.6
154.2
232.1
Seasonal Adjustments Example
Seasonality Adjusted Forecast
250
250
200
200
150
Demand
100
Unadjusted
Forecast
Demand
Demand
Unadjusted Regression Forecast
150
Demand
50
50
0
0
1
3
5
7
9 11 13 15
Period
Adjusted
Forecast
100
1
3
5
7
9
Period
11 13 15
Exercise
• Smith Company makes widgets. The
quarterly demand for its widget is
given in Exhibit A
• You have been asked to develop a
seasonal index for each quarter and
reforecast each quarter
Exhibit A
Year Quarter Demand
1
1
20
2
9.2
3
33.2
4
40
2
1
33.2
2
24
3
46.8
4
53.2
Exercise Table
Unadjusted
Quarterly Adjusted
Regression Demand/ Seasonal Regression
Period Year Quarter Demand Forecast Forecast
Index
Forecast
1
1
1
20
16.4
1.22
1.09
17.8
2
2
9.2
21.0
0.44
0.52
11.0
3
3
33.2
25.6
1.30
1.18
30.2
4
4
40
30.2
1.33
1.21
36.5
5
2
1
33.2
34.8
0.95
1.09
37.8
6
2
24
39.4
0.61
0.52
20.6
7
3
46.8
44.0
1.06
1.18
51.9
8
4
53.2
48.6
1.10
1.21
58.8
Click here to check your answer
Summary
• Deseasonalizing forecasts is effective for
– Short-term forecasting
– Comparability
– Detecting trend changes early
• The Seasonal Index is the most simple
method for making seasonal adjustments
Reading List
• Armstrong, J. Scott. Principles of Forecasting: A Handbook for
Researchers and Practitioners. Norwell: Kluwer Academic
Publishers, 2001.
• Bozarth, Cecil C. and Robert B. Handfield. Introduction To Operations
And Supply Chain Management. New Jersey: Prentice Hall, 2006.
• DeLurgio, Stephen and Carl Bhame. Forecasting Systems For
Operations Management. Homewood: Irwin, 1991.
• Hylleberg, Svend. Modeling Seasonality. New York: Oxford Press,
1992.
• Hylleberg, Svend. Seasonality in Regression. Orlando: Academic
Press Inc., 1986.
Appendix A: Solution to Exercise
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.779
R Square
0.607
Adjusted R Square
0.541
Standard Error
9.787
Observations
8
ANOVA
df
SS
MS
F
886.881
886.881
9.259
95.783
Regression
1
Residual
6
574.699
Total
7
1461.580
Coefficients
Intercept
X Variable 1
Standard Error
t Stat
P-value
Significance F
0.023
Lower 95%
Upper 95%
Lower 95.0% Upper 95.0%
11.771
7.626
1.544
0.174
-6.888
30.431
-6.888
30.431
4.595
1.510
3.043
0.023
0.900
8.290
0.900
8.290
Appendix A: Solution to Exercise
Unadjusted
Quarterly Adjusted
Regression Demand/ Seasonal Regression
Period Year Quarter Demand Forecast Forecast
Index
Forecast
1
1
1
20
16.4
1.22
1.09
17.8
2
2
9.2
21.0
0.44
0.52
11.0
3
3
33.2
25.6
1.30
1.18
30.2
4
4
40
30.2
1.33
1.21
36.5
5
2
1
33.2
34.8
0.95
1.09
37.8
6
2
24
39.4
0.61
0.52
20.6
7
3
46.8
44.0
1.06
1.18
51.9
8
4
53.2
48.6
1.10
1.21
58.8