Filter and parameter uncertainty


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.

Could you please provide more details. What do you mean with


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).

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?

That is exactely what I am looking for. I am not sure is there a way to combine these two sources of uncertainty.

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.

Starting with tomorrow’s unstable version/Dynare 4.5 you can use the smoothed_state_uncertainty option to get the uncertainty about the smoothed state estimate.