Consider the example of the town of Lincoln, which was analyzed using a multiplicative model in Figure 7.14. Repeat the forecasts using the additive model, with the same smoothing constants.

FIGURE 7.14 The Holt-Winters Method for the Town of Lincoln Example

a. What is the value of MSE corresponding to the multiplicative model in Figure 7.12?
FIGURE 7.12 Holt's Method for the Curtis Distributors Example

b. What is the value of MSE corresponding to the additive model with the same smoothing constants?

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Example for the Holt-Winters Method 1 Gamma 0.6 Alpha 0.2 Beta 0.5 4. Period Observed s(t) T(t) C(t) Forecast Error 8216 6303.0 0.0 1.30 9196 6303.0 0.0 1.46 3768 3 6303.0 0.0 0.60 6303.0 4032 0.0 0.64 10 7481 8216.0 735.0 6190.2 -56.4 1.25 11 6. 7889 5988.5 -129.1 1.37 8949.2 1060.2 F(t+ 1)=(5(1)+T())C(t+1-p) 12 3996 -46.6 0.64 3502.8 6024.4 13 3764 5959.1 -55.9 0.63 3824.0 60.0 14 6664 5791.8 -111.6 1.19 7358.4 694.4 15 10 7011 5564.6 -169.4 1.31 7804.5 793.5 16 11 4356 5683.6 -25.2 0.71 3437.3 -918.7 17 27.3 12 3565 5649.8 -29.5 0.63 3592.3 18 HIH7.7/7.8 7.9 7.10 7.14 0 7.11 7.12 7.13 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 69 бб.6 0.3 75 68.5 1.1 66.9 -8.1 72 70.1 1.3 69.6 2.4 10 92 75.6 71.5 -20.5 -4.0 F(t+1) = S(t)+T(t) 79.0 83.6 11 83 79.8 3.8 12 94 85.7 4.8 -10.4 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 18 13 120 117.3 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 17 146 137.2 5.5 135.0 -11.0 23 18 143 142.8 5.5 142.7 -0.3 24 19 131 144.9 3.8 148.3 17.3 25 20 151 149.1 4.0 148.7 -2.3 26 7.7 7.8 7.9 7.10 7.11 7.12 0 E.