Bayesian Estimation of Wishart Autoregressive Stochastic Volatility Model
Ming Lin
WISE
Changjiang Liu
WISE
Linlin Niu
WISE
3/3/2013 11:58:12 AM
Abstract:
The Wishart autoregressive (WAR) process is a powerful tool to model multivariate stochastic volatility (MSV) with correlation risk and derive closed-form solutions in various asset pricing models. However, making inferences of the WAR stochastic volatility (WAR-SV) model is challenging because the latent volatility series does not have a closed-form transition density. Based on an alternative representation of the WAR process with lag order p=1 and integer degrees of freedom, we develop an effective two-step procedure to estimate parameters and the latent volatility series. The procedure can be applied to study other varying-dimension problems. We show the effectiveness of this procedure with a simulated example. Then this method is used to study the time-varying correlation of US and China stock market returns.
Keyword: 
Bayesian posterior probability, Markov chain Monte Carlo, Multivariate stochastic volatility, Sequential Monte Carlo, Wishart autoregressive process