Hp_filtered and not hp_filtered moments: why similar means?


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

HP-filtering will always demean the data. What Dynare reports is the mean of the unfiltered data.

Thank you !

how do you see the moments of the filtered data, then? thanks

I don’t understand the question. The filtered second moments are displayed and the filtered first moments are always 0