Dear all,

Can one difference some explanatory variables but not the others? Or if one explanatory variable is differenced then all of them need to be differenced? Is it a statistical issue or rather an interpretative one?

My situation is that I first-order differenced all my explanatory variables except one which would require second-order differencing to be stationary. Thing is, I can induce stationarity on this variable by calculating and removing the trend, thus I don't see a point in second-order differencing it since then I would lose one more observation. Now, would having one variable in my OLS regression not differenced (still stationary though) cause some calculation issues, interpretation issues, etc.? As well, if I do need to difference them all does it need to be the same order differencing, that is, can variable x1 be first-order differenced whereas variable x2 second-order differenced?

Thank you.