On the modelling and forecasting multivariate realized volatility: Generalized Heterogeneous Autoregressive (GHAR) model

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. We propose to employ a system of seemingly unrelated regressions to capture the information. The newly proposed generalized heterogeneous autoregressive (GHAR) model is tested against natural competing models. In order to show the economic and statistical gains of the GHAR model, portfolio of various sizes is used. We find that our modeling strategy outperforms competing approaches in terms of statistical precision, and provides economic gains in terms of mean-variance trade-o. Additionally, our results provide a comprehensive comparison of the performance when realized covariance and more efficient, noise-robust multivariate realized kernel estimator, is used. We study the contribution of both estimators across different sampling frequencies, and we show that the multivariate realized kernel estimator delivers further gains compared to realized covariance estimated on higher frequencies.