Question

1. RDN’s sales of cable modem in San Mateo, California, for the months of January through April were as follows:

January	February	March	April
Y1	Y2	Y3	Y4

Suppose the Y values are deccreasing steadily from January through April. This means that Y1>Y2>Y3>Y4. The Holt’s model is used to make forecasts. Determine the answer that could be the forecasts for May, June, July: F(May), F(June), and F(July). [Observe the forecasts and decide which of the four options is the one that was produced by the Holt’s model]. No calculation is needed.

      a.    F(May) = 73, F(June) = 76, F(July) = 70

      b.   F(May) = 73, F(June) = 70, F(July) = 65

      c.   F(May) = 73, F(June) = 72, F(July) = 71

d.  F(May) = 73, F(June) = 76, F(July) = 79

Answer 1

We are given Y1 > Y2 > Y3 > Y4, i.e., it has a decreasing trend. Hence, none of the forecast can be greatr than its previous period value.

(a) F(May) = 73, F(June) = 76, F(July) = 70. In this forecast, F(June) = 76 > F(May) = 73, which contradicts the above trend. Hence, it can not be true

(b) F(May) = 73, F(June) = 70, F(July) = 65. This is more likely the case since, the trend is declining as per the principle of exponential smoothing. In other words, it seems that a weighted average of level and trend is applied to generate these forecasts.

(c) F(May) = 73, F(June) = 72, F(July) = 71. This series of forecast also shows declining trend, but the underlying weights seem to be linear and hence, this forecasts are not likely. Most likely, the level is only adjusted here which should not be the case.

(d) F(May) = 73, F(June) = 76, F(July) = 79. Here, the forecasts have positive trend which is not possible from a series which has a declining trend. Hence, this option is not valid.

Therefore, option (b) seems to provide valid forecasts with Holt's model.