Forecasting Realized Volatility Matrix With Copula Based Models
Multivariate volatility modeling and forecasting are crucial in financial economics. This paper develops a copula based approach to model and forecast realized volatility matrices. The proposed copula based time series models can capture the hidden dependence structure of realized volatility matrices. Also, this approach can automatically guarantee the positive definiteness of the forecasts through either Cholesky decomposition or matrix logarithm transformation. In this paper we consider both multivariate and bivariate copulas; the types of copulas include Student's t, Clayton and Gumbel copulas. In an empirical application, we find that for one day ahead volatility matrix forecasting, these copula based models can achieve significant performance both in terms of statistical precision as well as creating economically mean variance efficient portfolio. Among the copulas we considered, the multivariate t copula performs better in statistical precision, while bivariate t copula has better economical performance.