Bayesian semiparametric multivariate realized GARCH modeling

This paper introduces a novel Bayesian semiparametric multivariate GARCH framework for modeling re- turns and realized covariance, as well as approximating their joint unknown conditional density. We extend existing parametric multivariate realized GARCH models by incorporating a Dirichlet Process mixture of countably infinite normal distributions for returns and (inverse-)Wishart distributions for realized covariance. This approach captures time-varying dynamics in higher-order conditional moments of both returns and realized covariance. Our new class of models demonstrates superior out-of-sample forecasting performance, providing significantly improved multiperiod density forecasts for returns and realized covariance, and competitive covariance point forecasts.