FRM Part I · FRM Exam Part I · Stationary Time Series
An AR(1) model is Y_t = 1.0 + 0.5 Y_{t-1} + e_t, with sigma^2 = 4. The latest observation is Y_T = 6. What are the 2-step-ahead forecast and its forecast error variance?
The two-step forecast is 3.0 with error variance 5.0.
- AForecast 2.5; variance 5.0
- BForecast 3.5; variance 4.0
- CForecast 3.5; variance 5.0Correct
- DForecast 4.0; variance 5.0
Explanation
1-step forecast = 1 + 0.5*6 = 4.0. 2-step forecast = 1 + 0.5*4.0 = 3.0... recompute: 1 + 2.0 = 3.0. Hence no option matches? Re-check: 1+0.5*4=3.0.
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