Using Multivariate GARCH for Consistent Covariance Estimates

Summary

The question asks whether consistent covariance estimates require every asset’s volatility to use the same model and parameter values, and what to do when assets appear to follow different volatility processes. The responses point toward a full multivariate GARCH model, which models the assets’ conditional volatilities and their co-movement within one joint framework. They also mention constant-correlation approaches and direct the reader to treatments of multivariate volatility models.

The answers do not explain the mathematical consistency condition, compare model specifications, or resolve whether identical parameter estimates across assets are necessary. They offer modeling directions and references rather than a worked procedure. A joint model is presented as a possible way to handle cross-asset covariance, but the document gives no empirical evidence or guidance on choosing among multivariate GARCH variants when individual assets behave differently.

Key ideas

• The question distinguishes using the same model family from imposing identical volatility parameters across assets.
• A full multivariate GARCH model is suggested for joint volatility and covariance modeling.
• A constant-correlation approach is mentioned as another possible framework.
• The responses provide references but do not specify a consistency condition or model-selection procedure.

Tags

# Obtaining a consistent covariance matrix for stochastic volatility processes


# Obtaining a consistent covariance matrix for stochastic volatility processes












What is the condition for underlying stochastic volatility processes to give a consistent covariance matrix?

I read in Hull that in order to have a consistent covariance matrix, volatility parameters should be estimated using same model. Does that mean, for example, if I am using a Garch(1,1) model with some parameters, I should use the same parameters for all underlying? Or it is just enough to have Garch(1,1) and not necessarily the same parameters.

In either case, what would be a solution if the underlyings obviously fall under different models?

## Answer by Richi Wa (score 2)

https://quant.stackexchange.com/a/7660

I am not an expert in this field, but it would be best to consider a full multivariate GARCH model. This paper by Engle and Sheppard should be a good start.

I think the constant correlation matrix approach is covered to a certain extent too. I hope this helps.

## Answer by StayFoolish (score 0)

https://quant.stackexchange.com/a/10757

Yes, multivariate GARCH is what you should consider. Imho, you can look at a book, analysis of financial time series, by Ruey S. Tsay, in chapter 10, they discussed multivariate volatility models. You can google this book, download the pdf of second edition, hope it helps.

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