Multivariate volatility forecasting (GARCH) I have to analize 19 asset class, in order to make a volatility forecasting for each one. I know that with the EGARCH model (with the help of MATLAB) I can forecast volatiity, but only for 1 asset class (univariate analysis). Is there a Matlab version of EGARCH for multivariate analysis, or something that allow me to forecast volatility for all 19 asset class together?
I'm new in the econometrics world and in Matlab, I'm doing my thesis work.
 A: I don't now about Matlab but here is what I can tell about modelling the conditional variance-covariance matrix of a multivariate time series.
There are two nice overview papers of multivariate GARCH models:


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*Bauwens, Luc, Sébastien Laurent, and Jeroen VK Rombouts. "Multivariate GARCH models: a survey." Journal of applied econometrics 21.1 (2006): 79-109.

*Silvennoinen, Annastiina, and Timo Teräsvirta. "Multivariate GARCH models." Handbook of financial time series. Springer Berlin Heidelberg, 2009. 201-229.


I have personally tried the DCC model which is simple and easy to estimate (the latter property becomes important when you are working with more than two or three variables). The DCC model is also quite flexible with respect to the model choice for the variances of each of the variables (the diagonal elements of the variance-covariance matrix). You can, for example, choose an EGARCH model for one of the series, a FIGARCH for another etc., ect. There are also extensions of the DCC model allowing for asymmetries (the ADCC model)


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*Cappiello, Lorenzo, Robert F. Engle, and Kevin Sheppard. "Asymmetric dynamics in the correlations of global equity and bond returns." Journal of Financial econometrics 4.4 (2006): 537-572.


or different dynamics in different groups of time series (the FDCC model)


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*Billio, Monica, Massimiliano Caporin, and Michele Gobbo. "Flexible dynamic conditional correlation multivariate garch models for asset allocation." Applied Financial Economics Letters 2.02 (2006): 123-130.


The latter will be especially relevant if you are analyzing groups of assets where the assets within a group are somehow similar. However, DCC has received some serious critique:


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*Caporin, Massimiliano, and Michael McAleer. "Ten things you should know about the dynamic conditional correlation representation." Econometrics 1.1 (2013): 115-126.


Nevertheless, it is a widely used model with the original paper 


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*Engle, Robert. "Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models." Journal of Business & Economic Statistics 20.3 (2002): 339-350.


having received over 3500 citations (as counted in Google Scholar).
The R implementation in "rmgarch" package is very good, in my opinion:


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*Very broad choice of univariate GARCH specifications (the first step of building the DCC model)

*Broad choice of error distributions

*Broad choice of estimation techniques (optimization routines)

*Parallell computing available

*...and many more useful features

