# Winter’s method assumes a multiplicative seasonality but an additive trend. For example, a trend of…

Winter’s method assumes a multiplicative seasonality but an additive trend. For example, a trend of 5 means that the base will increase by 5 units per period. Suppose there is actually a multiplicative trend. Then (ignoring seasonality) if the current estimate of the base is 50 and the current estimate of the trend is 1.2, we would predict demand to increase by 20% per period. Ignoring seasonality, we would thus forecast the next period’s demand to be 50(1.2) and forecast the demand two periods in the future to be 50(1.2)^{2}.

If we want to use a multiplicative trend in Winter’s method, we should use the following equations:

a Determine what I and II should be.

b Suppose we are working with monthly data and month 12 is a December, month 13 a January, and so on. Also suppose that L_{12} = 100, T_{12} = 1.2, s_{1} = 0.90, s_{2} = 0.70, and s_{3} = 0.95. Suppose x_{13} = 200. At the end of month 13, what is the prediction for x_{15}? Assume α = β = γ =0.5.