Referring to this Post: What are the stationarity requirements of using regression with ARIMA errors for inference? I would like to seek a confirmation of the below practice:
The situation is as below:
1) I am trying to form a Multiple Regression with ARIMA errors
2) Y = B0 + B1X1 + B2X2 + e, where e is modelled with ARIMA.
3) Y, X1, and X2 are all NON-STATIONARY series.
4) Y and X1 are cointergated; but Y and X2 are NOT cointergated.
a)- Do I merely need to do differencing (or do what so ever) to make X2 become stationary, but no need to do so for Y and X1 ?
So the model will simply become Y = B0 + B1X1 + B2D(X2,1) + e , where e is modelled with ARIMA?
b)- If this is the case, does it mean that: as long as the variables are cointegrated, ARIMA errors can fix the non-stationary problem? So the ARIMA error is somehow another way of "Error Correction"?
But from my gut feeling, regression between non-stationary series may generate a spurious regression problem, it makes R2 extremely high, which implies less error is composed in such model. With less error, even though an ARIMA-error term is added, it may not solve the problem as error is merely contributing a small part...
So, I am not convinced with this method and it seems making all Y and Xs become stationary is the only way to do regression, no matter with or without ARIMA error terms. What do you guys think?