Multivariate range-based EGARCH models

The dynamic conditional correlation (DCC) and co-range models are two main frameworks used to incorporate range-based univariate volatility. Using the two approaches, we construct novel multivariate range-based EGARCH (REGARCH) models: a DCC-REGARCH and co-range REGARCH (CRREGARCH) model, and a co-range CARR (CRCARR) model. We compare these models with five existing models over twelve forecast horizons, ranging from one to twelve weeks, covering currencies and ETFs. Among the eight models, the DCC-REGARCH and CRREGARCH models show the best performance in out-of-sample forecasting of the variance-covariance matrix across a range of market conditions and forecast horizons. These models also generate the lowest variance and turnover for global minimum-variance (GMV) portfolios in the majority of cases.