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

A time series follows the process X_t = 0.6 X_{t-1} + e_t, where e_t is white noise with variance 4. Which statement about this process is correct?

It is a stationary AR(1) process. The characteristic equation 1 - 0.6B = 0 has root 1.67, outside the unit circle, so stationarity holds. The positive sign of the coefficient does not affect stationarity; only its absolute value being below one matters.

  1. AIt is an AR(1) process that is stationary because |0.6| < 1Correct
  2. BIt is an MA(1) process that is always stationary
  3. CIt is an AR(1) process that is non-stationary because the coefficient is positive
  4. DIt is an ARMA(1,1) process that is invertible
  5. It is an AR(2) process with a unit root

Explanation

The process regresses X_t on its own previous value, so it is AR(1). The root of 1 - 0.6B = 0 is B = 1/0.6 = 1.67, which lies outside the unit circle, so the process is stationary. The sign of the coefficient is irrelevant to stationarity.

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