DCC-HEAVY: A multivariate GARCH model with realized measures of variance and correlation

This paper proposes a new class of multivariate volatility model that utilising high-frequency data. We call this model the DCC-HEAVY model as key ingredients are the Engle (2002) DCC model and Shephard and Sheppard (2012) HEAVY model. We discuss the models' dynamics and highlight their differences from DCC-GARCH models. Specifically, the dynamics of conditional variances are driven by the lagged realized variances, while the dynamics of conditional correlations are driven by the lagged realized correlations in the DCC-HEAVY model. The new model removes well known asymptotic bias in DCC-GARCH model estimation and has more desirable asymptotic properties. We also derive a Quasi-maximum likelihood estimation and provide closed-form formulas for multi-step forecasts. Empirical results suggest that the DCC-HEAVY model outperforms the DCC-GARCH model in and out-of-sample.