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I used quantile regression for my research. My variables were significant but my pseudo r was low. So I tested for cointegration.

All my variables are I(1) and when I run the models with raw (nonstationary) data, the residuals are stationary at level. I believe this means my variables are cointegrated.

What should I do about the cointegration? What should my next step be?

Not using quantile regression is not an option. I used OLS for the residual testing. And I am using EViews.

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Vector error correction model (VECM) is appropriate for cointegrated data. The model only contains I(0) variables*, so no special treatment w.r.t order of integration is needed. You could use quantile regression techniques to estimate the model equations if you like.

*While the error correction term consists of I(1) variables, they enter in a fixed linear combination that is I(0).

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