FRM Part I · FRM Exam Part I · Nonstationary Time Series
A linear trend model for quarterly revenue (in USD millions) is estimated as Y_t = 40 + 2.5 t, with t = 1 in the first quarter of the sample. The sample has 60 observations. What is the forecast for revenue 4 quarters after the end of the sample (t = 64)?
The forecast is 200.0 million. Substitute t = 64 into the fitted trend: 40 + 2.5 × 64 = 200. The horizon is four quarters beyond the 60th observation, so t equals 64, not 60 or 65.
- A190.0
- B200.0Correct
- C202.5
- D160.0
Explanation
Forecast at t = 64: 40 + 2.5 × 64 = 40 + 160 = 200.0. Using t = 60 gives 190, which ignores the 4-quarter horizon. Forgetting the intercept gives 160. Using t = 65 gives 202.5, which is an off-by-one error.
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