I am using a calibrated model, and I am trying to replicate the observed variables with the smoothed shocks. I was trying to do that, but I had dissimilarities from the observed (and smoothed variables).
Eventually, I noticed that the difference was the “initial value” of the variable, as can be derived from shock decomposition. It made sense, as this is the portion of the variable that is not attributed to any shocks. I added that, and now the two series are exactly the same. Is there any better way to do that? Is this how I suppose to run it?