FRM Part I · FRM Exam Part I · Nonstationary Time Series
An analyst models monthly sales of a firm with the linear trend model y_t = 50 + 2.5t + e_t, where t = 1 in the first month of the sample. Based on this model, what is the forecast of sales for t = 41?
The forecast is 152.5. Substituting t = 41 into the linear trend gives 50 plus 2.5 times 41, which is 50 plus 102.5. The error term has an expected value of zero, so it does not change the point forecast.
- A152.5Correct
- B150.0
- C102.5
- D155.0
Explanation
The forecast is 50 + 2.5 x 41 = 50 + 102.5 = 152.5. Option 102.5 omits the intercept. Option 150 uses t = 40, and 155 uses t = 42.
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