IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Core concepts of time series models
For an AR(1) process with phi = 0.6 and white noise variance 16, what is the variance of the two-step-ahead forecast error?
The variance is 21.76. The two-step forecast error equals the new noise at t+2 plus 0.6 times the noise at t+1, so its variance is 16 times (1 + 0.36), which equals 21.76.
- A16.0
- B21.76Correct
- C25.0
- D32.0
- 10.24
Explanation
The two-step error is e_{t+2} + phi e_{t+1}, with variance sigma^2(1 + phi^2) = 16 x 1.36 = 21.76. Option 16 is the one-step error variance. Option 25 comes from using (1+phi)^2... no, 16 x 1.5625 is not correct here.
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