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I am curious. What are the typical uses of Multivariate GARCH models (BEKK, O-GARCH, DCC, etc) in practical finance applications?

You forgot GO-GARCH

If I'd try to list all of them, I'd probably run out of blackboard space.. so I just said (BEKK, O-GARCH, DCC, etc). In think only in the last 10 years people have come up with more than a dozen interesting MGARCH models and their extensions. So, I am curious if anyone actually successfully applies them in practice. Forecasting Value at Risk perhaps? Portfolio optimization? CAPM Betas? Something else?

These are the usual implications but they have also been applied to model stock returns, build-in indices. These do a pretty good job in practice and usually the difference is from the assumptions on the var-covar matrix.

I'd be interested to know what sort of step sizes people were using (tick, hour, week, quarter etc.) and how many steps (i.e. the term of the projection)

I mostly used DCC and DCC variants with daily observations.

I never used any GARCH models but to me they seem to be inferior to multivariate stochastic volatility models. You can very easily have a Heston type Multidimensional stochastic volatility model in which you could use PCA and work with resulting one dimensional principal components. For example even though you have an asset vector of 120 dimensionss, you could just use ten principle components and multiply their eigenvalues by a common or different stochastic volatility. We can kill the dimensionality by taking projection of 120 dimensional vector on ten eigenvectors that span most of the space in 120 dimensions and then filter each of them. We could then use MLE maximization to calibrate parameters of each principle component to the market data. It is also possible to possible to include negative correlation between stochastic volatility and associated eigenvector. So we have multidimensional simulation, nonlinear filtering and optimization to cope with the problem.I hinted at such a filtering technique in my stochastic basis spreads paper and I will add a lot more about it in the new version of my paper.