discrepancy between Shock decomposition and FEVD

[Jesse]

Dear Johannes,
Thank you very much for your helpful suggestion and guidance last time.
I just have 2 questions.
1. I have been told that one reason that causes discrepancy between historical shock decomposition and forecast error variance decomposition is that Kalman filter which decomposes forecast error variance has filtered the structural shocks belonging to some frequencies, I am wondering that does shocks belonging to long term frequency data is more likely to be filtered by Kalman filter or shocks belonging to short term frequency data is more likely to be filtered by Kalman filter?
2. why forecast horizons smaller than infinity in the FEVD cannot easily be compared to the historical decomposition results?
Thank you very much and look forward to hearing from you.
Kind regards,
Jesse

[jpfeifer]

1. This is not true. The Kalman filter is not a statistical filter in the sense that it filters out particular frequency components. It's called a filter, because it solves the "filtering problem" of best predicting the values of the unobserved states (in the class of linear Gaussian models).
2. The historical decomposition at any point in time shows the contribution of all previous realizations of a particular type shock. So the contribution of TFP shocks at time 10 consists of the effect of the TFP shock at t=1, t=2, ..., t=10. In constrast the FEVD at horizon 1 only asks about the relative contribution of shocks in the next period on the forecast error between today and tomorrow. That is a different question, because only the effect of shocks in 1 period is considered.