IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Core concepts of time series models
A time series X_t satisfies X_t = 0.6 X_{t-1} + e_t, where e_t is white noise. Which statement about this process is correct?
The process is a stationary AR(1) model. An AR(1) with coefficient a is stationary exactly when the absolute value of a is below 1, and 0.6 satisfies this. The noise variance and the sign of the coefficient do not affect stationarity.
- AIt is a stationary AR(1) process because |0.6| < 1Correct
- BIt is a non-stationary AR(1) process because the coefficient is positive
- CIt is an MA(1) process with parameter 0.6
- DIt is an ARIMA(1,1,0) process
- It is a stationary process only if the white noise variance is below 1
Explanation
An AR(1) process X_t = a X_{t-1} + e_t is stationary when |a| < 1. Here a = 0.6, so it is stationary. The sign of the coefficient does not decide stationarity, and the noise variance is irrelevant to it.
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