We introduce a methodology for dynamic modelling and forecasting of realized covariance matrices based on generalization of the heterogeneous autoregressive model (HAR) for realized volatility. Multivariate extensions of popular HAR framework leave substantial information unmodeled in residuals....

This paper compares multivariate and univariate GARCH models to forecast portfolio value-at-risk (VaR). We provide a comprehensive look at the problem by considering realistic models and diversified portfolios containing a large number of assets, using both simulated and real data. Moreover, we...

This paper disentangles the added value of using high-frequency-based (realized) covariance measures on multivariate volatility forecasting into two pillars: the realized variances and realized correlations and quantifies the corresponding economic gains using a broad set of portfolio...

Normal distribution of the residuals is the traditional assumption in the classical multivariate time series models. Nevertheless it is not very often consistent with the real data. Copulae allows for an extension of the classical time series models to nonelliptically distributed residuals. In...