Bayesian Semiparametric Modeling of Realized Covariance Matrices

This paper introduces several new Bayesian nonparametric models suitable for capturing the unknown conditional distribution of realized covariance (RCOV) matrices. Existing dynamic Wishart models are extended to countably infinite mixture models of Wishart and inverse-Wishart distributions. In addition to mixture models with constant weights we propose models with time-varying weights to capture time dependence in the unknown distribution. Each of our models can be combined with returns to provide a coherent joint model of returns and RCOV. The extensive forecast results show the new models provide very significant improvements in density forecasts for RCOV and returns and competitive point forecasts of RCOV.