# HP filter - theoretical moments

Hello all,

I would like to ask you for help with stochastic simulation.

What I want to achieve is comparing the theoretical second moments to the ones from the data. This topic has already been covered in some threads here but I have a different question. I understand that the correct procedure seems to be applying the same transformation on the simulated series and the data. Let’s say I have a log-linearized model using the data for output, inflation and nominal interest rates. I transformed the data prior to estimation so they match the variables in the model. For output, I applied one-sided HP filter. Is it correct to use stoch_simul command with one_sided_hp_filter=1600 option to obtain the theoretical moments from the simulated series even if only one variables was HP filtered prior to estimation?

Thanks a lot!
Martin

This one is tricky. Estimating the model on one-sided HP-filtered data implies that the unfiltered data is matched by the model. In that case, you may compare the unfiltered moments of the model to the data moments for the variables entering the model for estimation.

Thank you for very much for the answer, professor. I would understand comparing unfiltered moments of the model to the data moments for, in this case, inflation and interest rates which were not HP filtered, just demeaned prior to estimation. Hence, they match the variables in the model. But what is the rationale behind treating the one-sided HP filtered output the same when comparing the moments?

The reason is that the filter is not part of the model. You input filtered data for output to the model and force the model to mimic that behavior. It would be odd to have the model try to mimic filtered data, but then again filtering that variable. That’s the reason why most often we use growth rates to estimate a model. The first difference filter is then used for the both the data and the model variables.