Why GJR-GARCH Needs a Multivariate Extension for Covariance

Summary

The document asks how to obtain a covariance matrix when modeling asset returns with an AR(1)-GJR-GARCH(1,1) specification. A univariate GARCH model estimates conditional volatility for an individual return series, but that alone does not model the relationships between multiple assets needed for a covariance matrix.

The answer recommends using a multivariate GARCH framework and names BEKK, VECH, and dynamic conditional correlation (DCC) models as options to investigate. It provides direction rather than equations, implementation guidance, or a comparison of the approaches. The appropriate model depends on the data and modeling goals, which the short exchange does not discuss.

Key ideas

• A univariate GJR-GARCH specification estimates conditional volatility, not cross-asset covariance.
• Estimating a covariance matrix requires a multivariate volatility model.
• BEKK, VECH, and DCC are multivariate GARCH approaches to consider.
• The document does not compare model assumptions or provide implementation details.

Tags

# Covariance matrix from GJR-GARCH?


# Covariance matrix from GJR-GARCH?












I am implementing a AR(1)-GJR-GARCH(1,1) model to some asset returns, and I would need to have a covariance matrix but I struggle to see how I can compute one from the model I used? I know I can have a volatility estimate with a GARCH model, but what about covariance?

## Answer by Fr1 (score 1)

https://quant.stackexchange.com/a/47180

You have to use a multivariate Garch indeed. Search for mGARCH versions like GARCH-BEKK or VECH GARCH or DCC.

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