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

A time series X_t follows the model X_t = 0.6 X_{t-1} + e_t - 0.4 e_{t-1}, where e_t is white noise. Which description of this process is correct?

It is an ARMA(1,1) process that is both stationary and invertible, because the AR coefficient 0.6 and the MA coefficient magnitude 0.4 are both less than one in absolute value, and no differencing is involved.

  1. AARMA(1,1), stationary and invertibleCorrect
  2. BARMA(1,1), stationary but not invertible
  3. CARMA(1,1), invertible but not stationary
  4. DARMA(2,0), stationary
  5. ARIMA(1,1,1), non-stationary

Explanation

The model has one autoregressive and one moving average term, so it is ARMA(1,1). Stationarity needs |0.6|<1 for the AR part, which holds. Invertibility needs |-0.4|<1 for the MA part, which also holds. No differencing is present, so it is not ARIMA with d=1.

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