Martin Ringo responds:
This is the wrong question. The analyst shouldnâ€™t be worried about whether the dependent or independent is stationary or non-stationary. The issue is the error term.
In the Box-Jenkins procedure(s) â€” or maybe I should call it paradigm â€” the non-stationary stuff is removed. To me that removal is what is interesting, and all the stuff that Messrs. Box and Jenkins do is the treatment of serial correlation. But be you structural econometrician or time-series statistician, you can merrily regression a stationary variable on a non-stationary variable. You merely have to recognize that there is no impunity in regression. So you still have to check the residuals to see if they behave in a roughly white noise manner.