Holt’s method assumes an additive trend. For example, a trend of five means that the level will increase by five units per period. Suppose that there is actually a multiplicative trend. For example, 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 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 Holt’s method, you should use equations of the form:
Lt = αYt + (1 - α)(I)
Tt = β(II) + (1 - β)Tt - 1
a. What should (I) and (II) be?
b. Suppose you are working with monthly data and month 12 is December, month 13 is January, and so on. Also suppose that L12 = 100 and T12 = 1.2, and you observe Y13 = 200. At the end of month 13, what is the forecast for Y15? Assume α = β = 0.5 and a multiplicative trend.