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Very well presented indeed.

I was wondering how it would be for the bi-variate (and consequently multi-variate) case….basically the idea of the covar matrix forecast evaluation which is very useful when assessing the fitness of a risk model in general.

Thanks.

Moving from univariate to multivariate evaluation needs an additional step. We reduce the dimension from matrix back to univariate series using aggregation. Basically, we construct a portfolio using the estimated covariance matrix, and then evaluate the variance of that portfolio. See here: http://www.stern.nyu.edu/rengle/EngleColacito.pdf for a relatively readable instructions and supportive theory.

Thanks for the blog, really enjoy reading them.

The rugarch package has forecast and rolling functions built in (Ghalanos, 2014). It might be interesting to see what happens when these forecast evaluations are done with out-of-sample data