Winters’ method assumes a multiplicative seasonality but an additive trend. For example, a trend of 5 means that the level will increase by five units per period. Suppose that there is actually a multiplicative trend. Then (ignoring seasonality) if the current estimate of the level is 50 and the current estimate of the trend is 1.2, the forecast of demand increases by 20% per period. So the forecast demand for the next period is 50(1.2) and forecast demand for two periods in the future is 50(1.2)2. If you want to use a multiplicative trend in Winters’ method, you should use the following equations (assuming a period is a month):

a. What should (I) and (II) be?
b. Suppose that you are working with monthly data and month 12 is December, month 13 is January, and so on. Also, suppose that L12 = 100, T12 = 1.2, S1 = 0.90, S2 = 0.70, and S3 = 0.95. If you have just observed Y13 = 200, what is the forecast for Y15 using α = β = γ = 0.5 and a multiplicative trend?

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