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MCS,PHD
Argosy University/ Phoniex University/
Nov-2005 - Oct-2011
Professor
Phoniex University
Oct-2001 - Nov-2016
Weekly income for Quiet Mental Breakdown, an online psychology firm, is provided below. Determine, on the basis of minimizing the mean square error, whether a three-period or four-period simple moving average gives a better forecast.
Forecasting Problem Set
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F-1 Weekly income for Quiet Mental Breakdown, an online psychology firm, is provided below. Determine, on the basis of minimizing the mean square error, whether a three-period or four-period simple moving average gives a better forecast.
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|
Week |
Income |
 |
 |
 |
 |
 |
 |
 |
|
1 |
980 |
 |
 |
 |
 |
 |
 |
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|
2 |
1040 |
 |
 |
 |
 |
 |
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|
3 |
1120 |
 |
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|
4 |
1050 |
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|
5 |
960 |
 |
 |
 |
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 |
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|
6 |
990 |
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 |
 |
 |
 |
 |
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|
7 |
1030 |
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|
8 |
1260 |
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|
9 |
1240 |
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|
10 |
1100 |
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F-2 Using the table above, what is your forecast for week 11 using a three-period weighted average with weights of .6, .3 and .1? The weights are stated from the most current time period to the oldest time period.Â
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F-3 Using the table above, with smoothing constants of α = .10 and then α = .30, forecast income for week 11 using exponential smoothing.
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Solutions
F-1 On the basis of minimizing the mean square error, the three-period simple moving average gives a better forecast (smaller MSE). Â
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|
Week |
Actual Value |
Moving Average |
Error |
Squared Error |
|
1 |
980 |
 |
 |
 |
|
2 |
1040 |
 |
 |
 |
|
3 |
1120 |
 |
 |
 |
|
4 |
1050 |
1046.67 |
3.33 |
11.11 |
|
5 |
960 |
1070.00 |
-110.00 |
12100.00 |
|
6 |
990 |
1043.33 |
-53.33 |
2844.44 |
|
7 |
1030 |
1000.00 |
30.00 |
900.00 |
|
8 |
1260 |
993.33 |
266.67 |
71111.11 |
|
9 |
1240 |
1093.33 |
146.67 |
21511.11 |
|
10 |
1100 |
1176.67 |
-76.67 |
5877.78 |
|
11 |
 |
1200.00 Â |
 |
MSE=114,355.6/7=16336.51 |
|
 |
 |
 |
 |
 |
|
Week |
Actual Value |
Moving Average |
Error |
Squared Error |
|
1 |
980 |
 |
 |
 |
|
2 |
1040 |
 |
 |
 |
|
3 |
1120 |
 |
 |
 |
|
4 |
1050 |
 |
 |
 |
|
5 |
960 |
1047.50 |
-87.50 |
7656.25 |
|
6 |
990 |
1042.50 |
-52.50 |
2756.25 |
|
7 |
1030 |
1030.00 |
0.00 |
0.00 |
|
8 |
1260 |
1007.50 |
252.50 |
63756.25 |
|
9 |
1240 |
1060.00 |
180.00 |
32400.00 |
|
10 |
1100 |
1130.00 |
-30.00 |
900.00 |
|
11 |
 |
1157.50 |
 |
MSE=107,468.8/6=17911.46 |
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F-2
|
Week |
Income |
 |
|
1 |
980 |
 |
|
2 |
1040 |
 |
|
3 |
1120 |
 |
|
4 |
1050 |
1082.0 |
|
5 |
960 |
1070.0 |
|
6 |
990 |
1003.0 |
|
7 |
1030 |
987.0 |
|
8 |
1260 |
1011.0 |
|
9 |
1240 |
1164.0 |
|
10 |
1100 |
1225.0 |
|
11 |
 |
1158.0 |
|
12 |
 |
 |
Example week 4: Â Â Â Â 980(.1)+1040(.3)+1120(.6)=1082
Example week 11: 1260(.1)+1240(.3)+1100(.6)=1158
F-3 Using the table, with smoothing constants of α = .10 and then α = .30, forecast income for week 11 using exponential smoothing.
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|
Week |
Income |
α = .10 |
 |
|
1 |
980 |
 |
 |
|
2 |
1040 |
980.00 |
 |
|
3 |
1120 |
986.00 |
1040(.1)+ 980(.9)= 986 |
|
4 |
1050 |
999.40 |
1120(.1)+ 986(.9)= 999.40 |
|
5 |
960 |
1004.46 |
1050(.1)+ 999.40(.9)=1004.46 |
|
6 |
990 |
1000.01 |
 960(.1)+1004.46(.9)=1000.01 |
|
7 |
1030 |
999.01 |
 990(.1)+1000.01(.9)= 999.01 |
|
8 |
1260 |
1002.11 |
1030(.1)+ 999.01(.9)=1002.11 |
|
9 |
1240 |
1027.90 |
1260(.1)+1002.11(.9)=1027.90 |
|
10 |
1100 |
1049.11 |
1240(.1)+1027.90(.9)=1049.10 |
|
11 |
 |
1054.20 |
1100(.1)+1049.10(.9)=1054.20 |
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|
Week |
Income |
α = .30 |
|
1 |
980 |
 |
|
2 |
1040 |
980.00 |
|
3 |
1120 |
998.00 |
|
4 |
1050 |
1034.60 |
|
5 |
960 |
1039.22 |
|
6 |
990 |
1015.45 |
|
7 |
1030 |
1007.82 |
|
8 |
1260 |
1014.47 |
|
9 |
1240 |
1088.13 |
|
10 |
1100 |
1133.69 |
|
11 |
 |
1123.58 |
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