When filtering simulated data?


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 ?


That is a very large point of debate, which has gotten a lengthy treatment in Pfeifer(2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE Models” sites.google.com/site/pfeiferecon/Pfeifer_2013_Observation_Equations.pdf.
Most people would argue that you need to treat your model and your data in the same way. But there is also the position that you build a stationary model just to model the frequency components of the filtered data. In this case, you treat the unfiltered model variables directly as the data equivalent. The cynical answer might be: do what the referee asks you to do.