# Regression with non-stationary data

I am doing time series regression (the form I prefer is what SAS calls regression with AR error a form of GLS that runs OLS on the residuals and that has various names in the literature). The problem is that in many cases the dependent variable is clearly non-stationary. I have read various authors disagree on the following points.

1)If your dependent variable is non-stationary and some, but not all of your predictors, are non-stationary can you run GLS regression on these or must all of the variables be non-stationary.

2) What happens if for example you dependent variable is integrated of order 1 (I[1]), one predictor is i[1] and a second I[2]. Do you difference all the variables to I[0] which will require some variables to be differenced different amounts. I am not even sure it is valid to run regressions when the order of integration is not the same among predictors [note I assume stochastic not deterministic non-stationarity here].

3) Analysis of co integration I have seen deal with two, and only two variables one the dependent variable. When you have multiple predictors, does co integration assume that all the variables are co integrated?

• Hi: regression using non-stationary predictors and response is only valid if the order ( by order, I mean I(1), I(2) whatever ) of the predictors and response are the same AND atleast one of the predictors is cointegrated with the response. otherwise, it's not correct to use it. Differencing all of the variablesin order to make them stationary (I(0)) and then using regression is an option but then the results will have an extremely odd interpretation so I don't recommend trying that approach. Commented Feb 23, 2019 at 1:20
• with respect to 3), johansen's procedure handles the case where there are multiple predictors on the RHS. It's a much less intuitive approach compared to Engle-Granger but EG is limited to the simple regression case. Commented Feb 23, 2019 at 1:22