I am trying to compare the data simulated from my calibrated model with empirical data.
Empirical data obviously displays a trend whereas the model simulated data is cyclical and displays mean-reverting processes. I would tend to filter my empirical data to extract the cyclical component and to keep my simulated data as it is, but it sounds wrong, because I am not applying the same transformation both to my simulated data and to the empirical data I compare them to.
So what would you recommend in that case ? Is the fact that the model simulated data does not display trends as in the empirical data bad news for my model ?