Consider the example of Figure 7.7, in which the smoothing constant was taken to be a 0 2. Repeat the calculations for smoothing constants between 0.1 and 0.9, in steps of 0.1.
a. Identify the a–value that achieves the smallest value of MSE.
b. Identify the a–value that achieves the smallest value of MAD.

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G H K 1 Exponential Smoothing Example 2 Alpha 0.2 Iratial valum S(1) - XD 4 Period t Observed S(O Fafecost Error Deviation Percent 4-week Moving Averoge A( Forecast Difference Deviotion Percent 6 73 73.00 79.60 73.00 960 7. 2 106 3 16 78.88 4 89 B0.90 86.00 10 11 12 13 14 15 16 17 18 106 85.92 80.90 25.10 25.10 24% 94.25 \86.00 -20.00 20.00 19% 6 113 9134 85.92 -2108 27.08 24% 96,00 4.25 -18.75 18.75 17% 101.00 96 Al = EX+Xe-1-Xr-2)+Xe-31114 4 S) - anlt) +(-at-1 26.27 26.27 96 92.27 91.34 66 87.02 92.27 95,25 101.00 35.00 35.00 104 9041 87.02 -16.98 1698 16% 94.75 95.25 -8.75 8.75 8% 10 73 86.93 90.41 17.41 17.41 24% 84.75 94.75 21.75 21.75 30% 11 77 84.94 86.93 993 993 13% 80.00 84.75 7.75 7.75 10% 12 119 91.76 84.94 -34.06 34.06 29% 93.25 80.00 -39.00 39.00 33% 13 84 90.20 91.76 7.76 7.76 88.25 93.25 925 9.25 11% 19 20 21 22 23 14 71 86.36 90.20 19.20 19.20 27% 87.75 88.25 17.25 17.25 24% 15 88 86.69 86.36 -1.64 1.64 2% 90.50 87.75 0.25 0.25 16 97 88.75 86.69 -10.31 10.31 11% 85.00 90.50 -6.50 6.50 17 69 84 80 88.75 19.75 19.75 29% 81.25 85.00 16.00 16.00 23% 18 117 91.24 84 80 -32 20 32.20 28% 92.75 81.25 -35.75 35.75 31% 24 19 80 88.99 91.24 11.24 1124 14% 90.75 92.75 12.75 12.75 16% 25 26 27 28 20 73 85.70 88 90 15.90 15.99 22% 84.75 90.75 17.75 17.75 24% MSE MAD MAPE MSE MAD MAPE For periods 5-20 391.99 17.47 19.7% 409.02 16.66 19.1 29. 7.7 G H K 1 Exponential Smoothing Example 2 Alpha 0.2 Iratial valum S(1) - XD 4 Period t Observed S(O Fafecost Error Deviation Percent 4-week Moving Averoge A( Forecast Difference Deviotion Percent 6 73 73.00 79.60 73.00 960 7. 2 106 3 16 78.88 4 89 B0.90 86.00 10 11 12 13 14 15 16 17 18 106 85.92 80.90 25.10 25.10 24% 94.25 \86.00 -20.00 20.00 19% 6 113 9134 85.92 -2108 27.08 24% 96,00 4.25 -18.75 18.75 17% 101.00 96 Al = EX+Xe-1-Xr-2)+Xe-31114 4 S) - anlt) +(-at-1 26.27 26.27 96 92.27 91.34 66 87.02 92.27 95,25 101.00 35.00 35.00 104 9041 87.02 -16.98 1698 16% 94.75 95.25 -8.75 8.75 8% 10 73 86.93 90.41 17.41 17.41 24% 84.75 94.75 21.75 21.75 30% 11 77 84.94 86.93 993 993 13% 80.00 84.75 7.75 7.75 10% 12 119 91.76 84.94 -34.06 34.06 29% 93.25 80.00 -39.00 39.00 33% 13 84 90.20 91.76 7.76 7.76 88.25 93.25 925 9.25 11% 19 20 21 22 23 14 71 86.36 90.20 19.20 19.20 27% 87.75 88.25 17.25 17.25 24% 15 88 86.69 86.36 -1.64 1.64 2% 90.50 87.75 0.25 0.25 16 97 88.75 86.69 -10.31 10.31 11% 85.00 90.50 -6.50 6.50 17 69 84 80 88.75 19.75 19.75 29% 81.25 85.00 16.00 16.00 23% 18 117 91.24 84 80 -32 20 32.20 28% 92.75 81.25 -35.75 35.75 31% 24 19 80 88.99 91.24 11.24 1124 14% 90.75 92.75 12.75 12.75 16% 25 26 27 28 20 73 85.70 88 90 15.90 15.99 22% 84.75 90.75 17.75 17.75 24% MSE MAD MAPE MSE MAD MAPE For periods 5-20 391.99 17.47 19.7% 409.02 16.66 19.1 29. 7.7

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a The exponential smoothing model is used in forecasting Use following formula to calculate the forecasted value in exponential smoothing model Where ... View the full answer