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I am running a model with 3 independent variables. I want to test for cointegration but I have some questions. My dependent variable is stationary I(1) and one of the independent variables is stationary I(1).The other two independent variables are stationary I(0). 1) Should I run engle granger cointegration test only for my dependent variable and my one I(1) independent variable? 2) Engle Granger applies to stationary I(0) series? I am asking because I have to run much more models like this. For example in another model the dependent is stationary I(0) and the two independent variables are stationary I(1). Should I run engle granger only for the two independent variables that are I(1) and then run an engle-granger for the dependent I(0) and the one independent I(0)? or is that wrong?

In general I want to know what happens with engle-granger cointegration if in a regression we run more than 2 variables and we want to check for cointegration when we have differences in integration. Should we check for cointegration only for I(1) series or should we also check for I(0) series? p.s. Don't tell me about Johansen, I want to run engle-granger.

Thanks in advance

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According to the Econometrics Analysis 7th Edition on Engle-Granger test, "Let yt denote the set of M variables that are believed to be cointegrated. Step one is to establish that the variables are indeed integrated to the same order. The Dickey–Fuller tests discussed in Section 21.2.4 can be used for this purpose. If the evidence suggests that the variables are integrated to different orders or not at all, then the specification of the model should be reconsidered."

So to your first two questions, I think you should exclude the I(0).

When your dependent variable is I(0), the co-integration cannot be performed as there is no trend in it.

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