  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.
