I want to compare the prediction capacity of multivariate models (MGARCH, VAR, SVAR, VECM...). One option to do this is by comparing its error metrics: the mean square error or any other between the predicted values and some test data.
However, I would also like to compare its predictive ability with hypothesis tests. In the univariate case there is the Diebold-Mariano test. There is even a multivariate version of this test, but it compares several predictions but not multivariate models.
I would like to know if you know of another test that allows this comparison between multivariate models. Or another method that allows to vectorize the prediction errors to compare the models.