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FRM Part I · FRM Exam Part I · Stationary Time Series

An analyst fits an AR(2) model y_t = 0.5 y_{t-1} + 0.3 y_{t-2} + e_t. Which statement about this process is most accurate?

The process is covariance stationary because the roots of its lag polynomial lie outside the unit circle. The coefficients sum to 0.8, below one, and the other AR(2) conditions hold. A positive coefficient sum does not imply nonstationarity, and shock variance is irrelevant.

  1. AIt is covariance stationary because the coefficients are such that the roots of the lag polynomial lie outside the unit circleCorrect
  2. BIt is nonstationary because the coefficients sum to a positive number
  3. CIt is not stationary because an AR(2) always has a unit root
  4. DIt is stationary only if the shock variance is below 1

Explanation

Stationarity depends on the roots of 1 - 0.5L - 0.3L^2 lying outside the unit circle. Here the coefficients sum to 0.8, below 1, and the conditions phi1+phi2<1, phi2-phi1<1 and |phi2|<1 hold. Shock variance does not affect stationarity.

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