. Holt’s method assumes an additive trend. For example, a trend of 5 means that the level will increase by 5 units per period. Suppose there is actually a multiplicative trend. This means that if the...

. Holt’s method assumes an additive trend. For example, a trend of 5 means that the level will increase by 5 units per period. Suppose there is actually a multiplicative trend. This means that if the current estimate of the level is 50, and the current estimate of the trend is 1.2, we would predict demand to increase by 20% per period. So we would 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 Holt’s method, we should use the following equations:




a. What should U and V be to make this a sensible forecasting method.


b. Suppose we are working with monthly data and month 12 is December, month 13 is January, and so on. Also suppose that the level and trend, right after observing December’s value, are L₁₂
= 100 and T₁₂
= 1.2, respectively. Then we observe Y₁₃
= 200. At the end of month 13, what is the forecast for month 14? For month 15? Assume
 =
 0.2.