After the estimation of my model, I want to see the fit of the model to data visually. What I did was to plot the filteredVariables (from oo_)together with the actual data. If they are close, then the fit is good. Am I right?

I also notice that the oo_.SmoothedVariables are always exactly equal to the actual data for the observable variables. Is it always ture?

It isn’t clear what is a good fit in absolute. If you want to compare the fit of one model with the fit of another one, you are better use the log data density and a posterior odds ratio.

As far as graphics are concerned, the smoothed shocks are probably more revealing: They should be distributed around zero without too much autocorrelation. If it’s not the case, you should try to understand why. In the same spirit, you should look at big shocks and try to related them to well known historical episodes.

It is always true for models without measurement errors.