GARCH Ecourse: SVAR-GARCH Question

[e1983]

Hi. I recently purchased the GARCH ecourse (which is fantastic). In the section on SVAR-GARCH models, I understand that it is a two stage process. VAR in the first stage and univariate GARCH models for the structural residuals that are fit to the first stage residuals. Is it possible to use a multivariate GARCH model in the first stage rather than a VAR? If so, wouldn't that allow the reduced form Ht covariance matrix to vary rather than be fixed as it is in a VAR?

Thanks

[TomDoan]

First, that's not an accurate description of what is happening. Yes, it's a two-step process, but the univariate GARCH processes are buried inside the likelihood calculation for the model---they apply to what are basically unobservable orthogonalized processes. (The "S" in the SVAR isn't applied at the VAR stage, but at the GARCH stage, so GARCH is working with the standard residuals, not the structural ones).

And no, you can't reverse those. The residuals from a GARCH model must be, to start, mean zero and serially uncorrelated. So the multivariate GARCH model on data like those (which wouldn't be expected to be serially uncorrelated) has to include a mean model which cleans up the serial correlation, such as a VAR.

[e1983]

Hi. Tom. Thanks for the response. I really appreciate it and it helped. Im trying to figure out how Anderson, Bollerslev, and Diebold and Vega (2007) estimate equation 4.1 (free link to the paper below). They said in the paper they implement the methodology in

This is a very crude replication of Roberto Rigobon & Brian Sack, 2003. "Spillovers Across U.S. Financial Markets," NBER Working Papers 9640, which identifies the structural shocks in a VAR via a GARCH model.

My confusion is that it seems like Anderson, Bollerslev, and Diebold and Vega (2007) take the residuals from a multivariate GARCH model as observable, whereas Rigobon and Sak (2003) take the residuals from a reduced form VAR as observable. However, both papers assume that the structural shocks are heterskedastic and follow a univariate GARCH process. Is that correct?

Here is a free link to paper

https://papers.ssrn.com/sol3/papers.cfm ... _id=949180


Again, thanks so much for you time and help.

[TomDoan]

No. Anderson, et. al are doing the same basic thing (just with additional regressors)---the univariate GARCH specifications are on the unobservable residuals orthogonalized by the SVAR.

[e1983]

Got it. Thanks so much.