I am not used to time series econometrics. If I understand well, before conducting a linear regression (the most basic possible), we need to ensure the stationarity of our data - particularly with (Augmented) Dickey-Fuller tests. Then, we need to fit the optimal ARMA(p,q) model to our stationary data.
Once we've fitted ARMA model to the data, we can do forecasts, however I don't really understand how we can use them in linear regressions. Do we need to take the residuals of the ARMA process (our series without AR or MA influence) as our "new" variables for our regression ? Do we loose much information by doing so ?
I understand that we fit the ARMA process on regression residuals to check their stationarity and ensure that we did not do a spurious regression. But I am not sure on how to use the ARMA before the regression !