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!

  • $\begingroup$ 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. $\endgroup$ – Jonas_Dim May 4 at 18:17

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