# Stationarity check in ARX

How to formally check stationarity condition in a regression in the form: $$y_{t}=\alpha_{1}y_{t-1}+\alpha_{2}y_{t-2}+\beta_{1}x_{t}+\varepsilon_{t} \ ?$$

In the case of AR(2) there are some restrictions on the $$\alpha$$ coefficients. But in the case of external regressors what is the test for the check? Thank you!

• As long as the stationarity conditions for the AR(2) are satisfied and the process for $x_t$ is stationary, you should be fine. So I would use the usual procedures to check wether $x_t$ is stationary. – Jonas_Dim May 4 at 18:17