Solved – Heteroscedasticity in VAR Residuals

I got some heteroscedasticity in the residuals of a VAR model (check the plot). As fas as I know, the VAR coefficients are still consistent. However, the standard errors are supposed to be not well estimated. I know Newey West adjustment of residuals or GARCH modelling of residuals' volatility, but I'm not sure if I can apply them to the VAR model. Does anyone has an Idea how I could deal with this issue? I use the VAR implementation of statsmodels in python.

You may try multivariate GARCH models for errors of a VAR process, there is no conceptual problem with that. In R, this can be done in "rmgarch" package that facilitates estimation of several different multivariate GARCH models (DCC-GARCH, GO-GARCH, Copula-GARCH, probably some others) with conditional mean specification allowed to be a VAR model. (Unfortunately, I do not know how to do that in Python.)

You may use HAC-robust standard errors, too.

The advantage of GARCH over HAC-robust standard errors is that you may get more precise point estimates of the VAR parameters if the conditional variance model is estimated accurately enough. The advantage of HAC-robust standard errors is that it is simpler and is not subject to misspecification of conditional variance model (as there is none).

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