IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Core concepts of time series models
A stationary AR(1) process has X_t - mu = 0.5 (X_{t-1} - mu) + e_t with mu = 40. Given X_10 = 48, what is the best forecast of X_12 at time 10?
The forecast is 42. The deviation from the mean at time 10 is 8, and for a two-step horizon it shrinks by 0.5 squared, which is 0.25, giving 2 above the mean of 40. The figure 44 is only the one-step forecast.
- A42.0Correct
- B44.0
- C46.0
- D24.0
- 20.0
Explanation
The k-step forecast is mu + alpha^k (X_n - mu). Here the deviation is 8, so the 2-step forecast is 40 + 0.25 x 8 = 42. The option 44 is the one-step forecast (40 + 0.5 x 8), which is the wrong horizon.
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