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

A stationary AR(1) process has autocorrelation at lag 1 equal to 0.5. What is its autocorrelation at lag 3?

The lag 3 autocorrelation is 0.125. In a stationary AR(1) process the autocorrelation at lag k equals the coefficient raised to the power k, and the lag 1 autocorrelation equals the coefficient 0.5, so the result is 0.5 cubed.

  1. A0.125Correct
  2. B0.150
  3. C0.250
  4. D0.500
  5. 0.375

Explanation

For an AR(1), rho_k = a^k, and rho_1 = a = 0.5. So rho_3 = 0.5^3 = 0.125. The value 0.375 comes from multiplying 0.5 by 3 instead of raising it to the power 3.

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