FRM Part I · FRM Exam Part I · Stationary Time Series
An AR(1) model has intercept 1.0 and coefficient 0.5. The latest observation is y_T = 4. What is the two-step-ahead forecast of y_{T+2}?
The two-step forecast is 2.5. Iterating the model, the one-step forecast is 1 + 0.5 times 4, which is 3.0, and the next step gives 1 + 0.5 times 3.0, which is 2.5. The forecast moves toward the unconditional mean of 2.
- A2.5
- B3.0
- C3.5Correct
- D4.0
Explanation
One step: 1 + 0.5(4) = 3.0. Two steps: 1 + 0.5(3.0) = 2.5. Wait, check: 1 + 1.5 = 2.5, so the correct value is 2.5 and the key matches option index 0.
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