Bayesian semiparametric multivariate stochastic volatility with application

In this article, we establish a Cholesky-type multivariate stochastic volatility estimation framework, in which we let the innovation vector follow a Dirichlet process mixture (DPM), thus enabling us to model highly flexible return distributions. The Cholesky decomposition allows parallel univariate process modeling and creates potential for estimating high-dimensional specifications. We use Markov chain Monte Carlo methods for posterior simulation and predictive density computation. We apply our framework to a five-dimensional stock-return data set and analyze international stock-market co-movements among the largest stock markets. The empirical results show that our DPM modeling of the innovation vector yields substantial gains in out-of-sample density forecast accuracy when compared with the prevalent benchmark models.