One side HP-filter and model fit to real data

Estimation ML/Bayesian estimation
#1

Dear professor jpfeifer,

I got three questions on one side HP-filter and model fit to real data:

First, when doing Bayesian estimation, the real data (e.g. real output “y”) are first seasonally adjust, then take the log of the data and apply the one-sided HP-filter. My question is we can not use the one-sided HP-filter in Eviews as it is two-sided HP-filter, it must be done in Matlab, right? Can you give me an example code for one-side HP-filter of Matlab?

Second, if variable of the code is written in level, the observation is then : yobs=log(y)-log(steadystate y), where yobs is oberved variable (the data after first seasonally adjust, take log, one-sided HP-filter), is this right?

Third, when judging whether the estimation result fit the real data well, as the variable of the code is in level, I add log_y in “Definition of variables” , use the code "stoch_simul(order=1,hp_filter=1600); log_y ", then compare the theoritical moments (S.D or Correlations) with the statistics of the real data, is this right?

Really hope for your reply which always help me a lot, thank you, professor.
Best.

#2
  1. Yes, you cannot use the two-sided filter. Matlab code is available at matlab/one_sided_hp_filter.m · master · Dynare / dynare · GitLab
  2. Yes, that matching is correct for a non-logged and non-demeaned variable.
  3. No, ist should be one_sided_hp_filter=1600 in the stoch_simul-command if you want to compare it to one-sided HP-filtered data.
#3

Thank you, professor, so stoch_simul(order=1,one_sided_hp_filter=1600); log_y " is correct, right?

#4

Dear professor, I am wandering if you can clearly explain to me why variables in log-linearization using hp_filter=1600, while variables in level using one_sided_hp_filter=1600in thestoch_simul` -command? I am really confused about the hp_filter option, always thank you and best wishes.

#5

It’s not about logs vs. levels. Your data and model treatments need to be consistent for meaningful comparisons. You said you used the one-sided HP filter for the data, so you should use it for the model as well.