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FRM Part I · FRM Exam Part I · Stationary Time Series

An analyst fits an AR(1) model y_t = 2 + 0.6 y_{t-1} + e_t to a stationary series, where e_t is white noise. The latest observation is y_T = 7. What is the one-step-ahead forecast of y_{T+1}?

The one-step-ahead forecast is 6.2. Substitute the last observation into the fitted AR(1) equation: 2 plus 0.6 times 7 equals 6.2. The unconditional mean of 5 applies only to long horizons, and omitting the intercept would give 4.2.

  1. A6.2Correct
  2. B4.2
  3. C9.0
  4. D5.0

Explanation

The one-step forecast is 2 + 0.6 × 7 = 2 + 4.2 = 6.2. Option 4.2 omits the intercept. Option 5.0 is the unconditional mean (2/0.4), which is the long-run forecast, not the one-step forecast. Option 9.0 adds 0.6 and 7 incorrectly after the intercept.

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