Consider the example of the new product at Curtis Distributors, which was analyzed using Holt's method in Figure 7.12. Repeat the forecasts using one smaller value of a than the value of 0.2 used in the figure, and also one larger value. Then do the same, using one smaller value of b than the value of 0.5 used in the figure, and also one larger value. (This means nine pairs of values in all, one of which is illustrated in the figure.)
FIGURE 7.12 Holt's Method for the Curtis Distributors Example

a. Which pair (a, b) achieves the smallest value of MSE?
b. Which pair (a, b) achieves the smallest value of MAD?

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H. 1 Example for Holt's Method 2 3 Alpha 0.2 Beta 0.5 4 Period Observed S(t) T(t) Forecast Error 66 66.0 0.0 бб.6 69 0.3 66.9 75 68.5 1.1 -8.1 1.3 72 70.1 69.6 2.4 -20.5 10 71.5 92 75.6 -4.0 F(t+1) = S(t)+T(t) 79.0 83.6 3.8 11 83 79.8 12 -10.4 94 85.7 4.8 90.5T()=B(S(1)-S(t-1))+(1-B)T(t-1) 99.7 13 8. 105 93.4 6.3 14 90 97.8 5.3 9.7 15 10 112 104.9 6.2 s(t) = ax(t) + (1-a)(S(t-1)+T(t-1) %3D 16 11 99 108.7 5.0 17 12 107 112.3 4.3 113.7 6.7 117.3 18 13 120 4.7 116.7 -3.3 19 14 114 120.4 3.9 122.0 8.0 20 15 138 127.0 5.2 124.3 -13.7 21 16 124 130.6 4.4 132.3 8.3 22 137.2 135.0 -11.0 17 146 5.5 23 18 143 142.8 5.5 142.7 -0.3 24 17.3 19 131 144.9 3.8 148.3 25 149.1 -2.3 20 151 4.0 148.7 26 7.8 7.9 7.10 7.11 7.12 0 7.7 E.