Efficient Bayesian estimation of a multivariate stochastic volatility model with cross leverage and heavy-tailed errors

Abstract

An efficient Bayesian estimation using a Markov chain Monte Carlo method is proposed in the case of a multivariate stochastic volatility model as a natural extension of the univariate stochastic volatility model with leverage and heavy-tailed errors. The cross-leverage effects are further incorporated among stock returns. The method is based on a multi-move sampler that samples a block of latent volatility vectors. Its high sampling efficiency is shown using numerical examples in comparison with a single-move sampler that samples one latent volatility vector at a time, given other latent vectors and parameters. To illustrate the proposed method, empirical analyses are provided based on five-dimensional S&P500 sector indices returns.