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.

Keywords:

• Bayesian inference
• Chinese stock market
• conditional constant correlations
• DIC
• MCMC
• multivariate GARCH and stochastic volatility
• prior for correlation matrix
• sector index
• WinBUGS

Acknowledgements

The authors gratefully appreciate helpful discussions from BUGS list, especially Paul Louisell and Andrew Millard's constructive suggestions about prior setting. We thank Prof. Grier, Meyer, Yu, Terasvirta and Liechty for their kind help. We thank the anonymous referees for the suggestions. This work was Financially Supported in part by Self-Determined Research Funds of ECUST from the Colleges’ Basic Research and Operation of MOE (WM0914017).

Notes

The WinBUGS package (the latest version is 1.4.3) as well as WinBUGS User Manual can be downloaded free of charge from http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/contents.shtml.

Standard normal distribution with mean 0 and deviation 1 can improve convergence.

For more details about model specification, please refer to WinBUGS User Manual.

The data were downloaded from http://finance.yahoo.com.

To save space, only part of results and plots are listed here. And all the results and source codes used in this paper are available from the author upon request.

For more details about convergence diagnose with the Gelman Rubin statistic module refer to WinBUGS User Manual.