Contrary to the moving-average (MA) model, the autoregressive model is not always stationary as it may contain a unit root.

Is AR process always stationary?

The AR(1) process is stationary if only if |φ| < 1 or −1 <φ< 1. This is a non-stationary explosive process. If we combine all the inequalities we obtain a region bounded by the lines φ2 =1+ φ1; φ2 = 1 − φ1; φ2 = −1. This is the region where the AR(2) process is stationary.

Is AR 1 weakly stationary?

As a weakly stationary process must have a finite constant variance, an AR(1) process is not stationary if |α|≥1 | α | ≥ 1 .