IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Applications of time series models
An actuary models the monthly claim inflation of an Indian motor insurer by the AR(1) process X_t = 0.6 X_{t-1} + e_t, where e_t is white noise with variance 16. What is the stationary variance of X_t?
The stationary variance is 25. For an AR(1) process the variance equals the noise variance divided by one minus the square of the parameter, so 16 divided by 0.64 gives 25.
- A16.00
- B25.00
- C40.00
- D10.24
- 44.44Correct
Explanation
For AR(1) with parameter a, Var = sigma^2/(1-a^2) = 16/(1-0.36) = 16/0.64 = 25. Check: 0.36*25+16 = 25, which holds. Therefore the correct value is 25. 16/0.36 = 44.44 uses a^2 incorrectly as the denominator; 16/0.4 = 40 uses 1-a.
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