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filter and parameter uncertainty

PostPosted: Tue Oct 25, 2016 11:46 am
by joff
Hi.

I am using Bayesian approach to estimate the so-called multivariate filter (MVF) model and obtain output gap estimates. My problem is that I would like to have bands around those estimates. However, it seems that the bands around smoothed gap given by Dynare account only for the parameter uncertainty and not for the filter uncertainty. Or am I missing something? Any help is appreciated.

Re: filter and parameter uncertainty

PostPosted: Tue Oct 25, 2016 5:55 pm
by jpfeifer
Could you please provide more details. What do you mean with
filter uncertainty
?

Re: filter and parameter uncertainty

PostPosted: Wed Oct 26, 2016 6:49 am
by joff
I was probably a bit imprecise. What I mean is the uncertainty regarding unobserved variables (like output gap) conditional on the observed variables and the parameters of the model being known. It seems to me that posterior dostribution of smoothed unobserved variables does not take this into account (it only takes into account the parameter uncertainty).

Re: filter and parameter uncertainty

PostPosted: Wed Oct 26, 2016 6:16 pm
by jpfeifer
What exactly are you looking for? Conditional on the parameters, we are talking about a linear Gaussian state space model. The variables are therefore characterized by a conditional mean and covariance (the first two moments are necessary for a multivariate normal distribution). The HPDI's of the smoothed variables show the dispersion of the conditional mean across parameter draws. You in contrast seem to be interested not in the first, but the second moments. What you are looking for is Var(X_t|Y_T), i.e. the uncertainty about a state X at time t given the full history of observations Y_T?

Re: filter and parameter uncertainty

PostPosted: Wed Oct 26, 2016 6:35 pm
by joff
That is exactely what I am looking for. I am not sure is there a way to combine these two sources of uncertainty.

Re: filter and parameter uncertainty

PostPosted: Thu Oct 27, 2016 7:42 pm
by jpfeifer
The combination of the two kinds of uncertainty is a conceptual problem for which I also do not have a quick answer. But from the Dynare perspective, I just notice that we do not compute the uncertainty bands around the smoothed state estimates. I will try to change that soon.

Re: filter and parameter uncertainty

PostPosted: Sun Nov 13, 2016 7:43 pm
by jpfeifer
Starting with tomorrow's unstable version/Dynare 4.5 you can use the
Code: Select all
smoothed_state_uncertainty
option to get the uncertainty about the smoothed state estimate.