Bayesian estimation and comparison of MGARCH and MSV models via WinBUGS

Abstract

This paper shows that Bayesian estimation and comparison of multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) and multivariate stochastic volatility (MSV) models with Markov Chain Monte Carlo methods could be straightforwardly and successfully conducted in WinBUGS package. And an algorithm based on the Cholesky decomposition is proposed to set as a prior for a correlation matrix. They are illustrated by applying three types of parsimonious MGARCH and MSV specifications nested in constant conditional correlations to weekly returns of five sector indexes of Shanghai Stock Exchange over the period of 28 June 2004 to 30 June 2008. Empirical results provide evidence for the superior performance of MSV models over MGARCH models and give support to the feasibility of the algorithm we presented. In addition, the estimation results also suggest the significant negative correlation between the persistency and the variability of volatilities in MSV models.