Forecasting variance decomposition vs historical decomposition


Hallo everyone
I have one question related to forecasting variance and historical decompositions in DSGE model
One of the different points btw these two methods is that forecasting variance decomposition is a out-of-sample based technique, whereas historical decomposition is a in-sample technique. So my question is that are the finding from this two different approaches exactly identical to each other? For example, in terms of forecasting variance decomposition, I find that technology is main driver of output fluctuation, then this finding would be identical to that by using historical decomposition?

I am looking forward to your answer soon


The variance decomposition is a theoretical and importantly asymptotic concept. It relies on shocks being orthogonal, i.e. uncorrelated. In contrast, in finite samples even theoretically uncorrelated shocks can show a correlation. For that reason, the historical shock decomposition can yield a different picture.


Dear Prof. Pfeifer

Thank you so much for your interesting explanations

So I can say that the finding from forecasting and historical decomposition might be either identical or different. My understanding is correct?

Best wishes


As I said above: in finite samples that is true.