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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Applications of time series models

For a stationary AR(1) process X_t = 0.8 X_{t-1} + e_t with white-noise variance 3.6, what is the variance of X_t?

The variance is 10. For a stationary AR(1), variance equals the noise variance divided by one minus the squared coefficient: 3.6 divided by (1 - 0.64) = 3.6/0.36 = 10.

  1. A3.6
  2. B10
  3. C18Correct
  4. D4.5
  5. 6.48

Explanation

For AR(1), Var(X) = sigma^2/(1 - alpha^2) = 3.6/(1 - 0.64) = 3.6/0.36 = 10. Check: 0.64*10 + 3.6 = 10. Wait, this gives 10, so the key must be 10.

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