FRM Part I · FRM Exam Part I · Stationary Time Series
An ARMA(1,1) model is Y_t = 2 + 0.7 Y_{t-1} + e_t + 0.2 e_{t-1}. The last observation is Y_T = 8 and the last residual is e_T = 1.5. What is the one-step-ahead forecast of Y_{T+1}?
The one-step-ahead forecast sets the future shock to zero and keeps the known residual: 2 plus 0.7 times 8 plus 0.2 times 1.5 equals 7.9. Ignoring the moving-average residual term would give 7.6, which is incorrect.
- A8.3Correct
- B7.9
- C7.6
- D8.6
Explanation
Forecast = 2 + 0.7(8) + 0.2(1.5) since E[e_{T+1}]=0. That is 2 + 5.6 + 0.3 = 7.9. Omitting the MA term gives 7.6; the correct value is 7.9.
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