I am trying to learn how to conduct regression with time series data [historically I have used univariate methods that is ESM or ARIMA - multivariate ARIMA simply is too time consuming to consider given the need to prewhiten]. I intend to use ARDL which is time series with autoregressive error with the added ability to do lags of the dependent or independent variable.

A question that I encountered before is if univariate analysis of variable (either dependent or independent) indicates that the variable is non-stationary do you difference it in regression as you would in ARIMA? Secondly, assuming you do difference variables, what do you do if the variables are integrated as of a different order. For example one is I[1] and another I[0]?

Does cointegration, something that is doubtful theoretically with our data, change any of this?