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

Consider the AR(2) process X_t = 1.2 X_{t-1} - 0.2 X_{t-2} + e_t. Which statement is correct?

The process is non-stationary because the characteristic polynomial 1 - 1.2z + 0.2z² has a root at z = 1, a unit root. The other root is 5, but one root on the unit circle is enough to break stationarity.

  1. AIt is stationary because both roots of the characteristic polynomial lie outside the unit circle
  2. BIt is stationary because the coefficients sum to less than 2
  3. CIt is non-stationary because one root of 1 - 1.2z + 0.2z^2 equals 1Correct
  4. DIt is non-stationary because the second coefficient is negative
  5. It is stationary because the coefficient of X_{t-1} exceeds 1

Explanation

The characteristic polynomial is 1 - 1.2z + 0.2z^2. At z=1 it gives 1 - 1.2 + 0.2 = 0, so z=1 is a root (the other is z=5). A root on the unit circle means a unit root, so the process is non-stationary. The negative coefficient is irrelevant.

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