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 stockmarket 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.

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Keywords Bayesian nonparametrics, Dirichlet process mixture, Markov chain Monte Carlo, stock-market co-movements
JEL Bayesian Analysis (jel C11), Semiparametric and Nonparametric Methods (jel C14), Forecasting and Other Model Applications (jel C53), Financial Econometrics (jel C58), General Financial Markets: General (jel G10)
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Journal Econometric Reviews
Zaharieva, M.D., Trede, M, & Wilfling, B. (2020). Bayesian semiparametric multivariate stochastic volatility with application. Econometric Reviews. doi:10.1080/07474938.2020.1761152