This thesis introduces a generalization of the Threshold Stochastic Volatility (THSV) model proposed by So, Li and Lam (2002) to a multivariate model , in which we call it the Multivariate Threshold Stochastic Volatility (MTHSV) model. The MTHSV model can model the asymmetry effect in mean and variance components simultaneously for the multivariate time series. Bayesian methods are adopted to estimate the model parameters. In order to sample from a com-plex joint conditional posterior density, MCMC methods are suggested to use. In particular, as a special case of MCMC methods, Gibbs sampler is employed in the Bayesian inference of this thesis. Kalman Filter, random-walk Metropo-lis algorithm and multi-move sampler have been applied in the implementation of the Gibbs sampler, and have go...[ Read more ]

This thesis introduces a generalization of the Threshold Stochastic Volatility (THSV) model proposed by So, Li and Lam (2002) to a multivariate model , in which we call it the Multivariate Threshold Stochastic Volatility (MTHSV) model. The MTHSV model can model the asymmetry effect in mean and variance components simultaneously for the multivariate time series. Bayesian methods are adopted to estimate the model parameters. In order to sample from a com-plex joint conditional posterior density, MCMC methods are suggested to use. In particular, as a special case of MCMC methods, Gibbs sampler is employed in the Bayesian inference of this thesis. Kalman Filter, random-walk Metropo-lis algorithm and multi-move sampler have been applied in the implementation of the Gibbs sampler, and have gotten a success in the estimation through the demonstration of simulation experiments except the algorithm of drawing Σ_η can be further improved. Four stock market indices have be applied to the model to demonstrate the empirical properties of the model. Asymmetry in mean and variance were observed in the stock indices data.