IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Core concepts of time series models
A stationary AR(1) model is X_t - 50 = 0.6(X_{t-1} - 50) + e_t, with white noise variance 16. The latest observation is x_100 = 60. What is the two-step-ahead forecast of X_102?
The two-step forecast is 53.6. For an AR(1) model the forecast reverts to the mean geometrically: 50 plus 0.6 squared times the deviation of 10 from the mean, which gives 50 + 3.6 = 53.6.
- A56.0
- B53.6Correct
- C58.0
- D59.6
- 51.0
Explanation
The h-step forecast is mu + phi^h (x_n - mu). Here 50 + 0.36 x 10 = 53.6. Using phi instead of phi squared gives 56.0, which is the one-step forecast, so it is wrong.
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