I don’t understand how is the model-generated data hp-filtered with the Dynare option hp_filter in the stoch_simul command. When I compare any simulated DSGE model with and without hp_filtering, I notice that the first order theoretical moments are similar for hp_filtered theoretical moments and for not hp_filtered theoretical moments.
However, when I hp_filter empirical data in Matlab using the hpfilter command, the hp_filtered empirical data does not display the same mean as the initial empirical data. I find this quite intuitive : a series with a positive time trend should display a higher mean than the cyclical component of this series.
So why do we get similar means for hp_filtered data and not hp_filtered data when simulating the model in Dynare ?
Any help would be much appreciated