Hi all,

I am trying to do a historical decomposition using the estimation output from a small open economy model…What I am thinking of is to feed in the oo._smoothedshocks into the model using simul_m. One thing that I want to ask is how the oo._smoothedshocks are obtained…Are these historical series of shocks obtained using estimates at the posterior mode or mean or median? And does that apply similarly to the decision rule oo._dr?

Also, what is the difference between Filteredvariables, smoothedvariables and updatedvariables?

I will be very grateful for any comment!


If you only computed the posterior mode, all derived series (smoothed, filtered, updated variables and shocks) and oo_.dr are computed at the posterior mode. If you ran Metropolis iterations, they are computed at the posterior mean.

For any variable of the model (y_t)
smootherd variable: E_{t|T} y_t
filtered variable: E_{t-1} y_t
updated variable: E_t y_t

See for example, Harvey’s book on Kalman Filter for the formulas.



Dear Michel,

Thank you so much for your explanation!