Consider the example of Figure 7.7, in which the smoothing constant was taken to be α = 0:2. Repeat the calculations for smoothing constants between 0.1 and 0.9, in steps of 0.1.
FIGURE 7.7: Worksheet for Exponential Smoothing Calculations

a. Identify the a-value that achieves the smallest value of MSE.
b. Identify the a-value that achieves the smallest value of MAD?

H. 1 Exponential Smoothing Example Initial value S(1) - X(1) Alpha 0.2 4 Period 4-week Moving Average Fafecast Observed st) Error Deviation Percent A(t) Forecast Difference Deviation Percent 6. 73.00 73 79.60 73.00 106 78.60 76 78.88 86.00 78.88 89 80.90 10 94.25 \86.00 94.25 9e A(t) = [X(t)+X(t-1)+X(t-2)+X[t-3)]14 106 85.92 80.90 25.10 -27,08 -4.St) - aalt) + (1-e)S(t-11 25.10 24% -20.00 20.00 19% 11 113 91.34 85.92 27.08 24% 96.00 -18.75 18.75 17% 12 92.27 91.94 96 101.00 13 26.27 26.27 40% 35.00 66 87.02 92.27 95.25 101.00 35.00 53% 14 104 90.41 87.02 -16.98 16.98 16% 94.75 95.25 -8.75 8.75 8% 15 86.93 90.41 10 73 17.41 17.41 24% 84.75 94.75 21.75 21.75 30% 16 84.94 11 77 86.93 9.93 9.93 13% 80.00 84.75 7.75 7.75 10% 17 12 119 91.76 84.94 -34.06 34.06 29% 93.25 80.00 -39.00 39.00 33% 18 90.20 93.25 13 84 91.76 7.76 7.76 9% 88.25 9.25 9.25 11% 19 14 71 86.36 90.20 19.20 19.20 27% 87.75 88.25 17.25 17.25 24% 87.75 20 15 88 86.69 86.36 -1.64 1.64 90.50 -0.25 0.25 21 22 16 97 88.75 86.69 -10.31 10.31 11% 85.00 90.50 -6.50 6.50 19.75 16.00 17 69 84.80 88.75 19.75 29% 81.25 85.00 16.00 23% 23 91.24 32.20 18 117 84.80 -32.20 28% 92.75 81.25 -35.75 35.75 31% 24 80 88.99 19 91.24 11.24 11.24 14% 90.75 92.75 12.75 12.75 16% 25 85.79 15.99 175. 17.75 20 75 88.99 15.99 22% 84.75 90.75 24% 26 27 MAPE MSE MAD MAPE MSE MAD 28 17.47 19.7% 19.1% For periods 5-20 391.99 409.02 16.66 29 7.7