Separation of variance and covariance forecasting:

Another important issue we cover is the separate analysis of the model with regard to variance and covariance forecasting. As already discussed in section  the results plotted in the univariate context determine the quality of the model for variance forecasting. The measures plotted in the multivariate context determine the quality of the model for variance and covariance forecasting. If it has been determined that the model has good performance in the univariate context but bad performance in the multivariate context - this must mean that some modifications are necessary only in the covariance forecasting aspect of the model. Aside from the latter important information - the analysis in the univariate context is based on far more data and helps give more robust estimates of variance forecasting performance by a model even at the 99% level where exceedence data is sparse. (Note how the figures m are noisier than figures u.)