Bayesian Semiparametric Multivariate Realized GARCH Modeling

ABSTRACT This paper introduces a novel Bayesian semiparametric multivariate GARCH framework for modeling returns 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, as well as competitive covariance point forecasts.