Cointegration and imposing AR terms

[PoachedWonk]

Hello,

I am dealing with what I believe to be cointegrated statistics (Johansen says cointegration is present) however, when regressing the model the error terms are not stationary.

One of the causes of this is autocorrelation in the dependent regressor. So by imposing an AR structure on the model, I do get stationarity of the error terms, but is this cooking the equation to make it stationary?

Thanks!