Research On Bayesian Analysis For Regime Switching GARCH Model And Its Application

Volatility is a very important character of financial time series. It can indicate the market's quality and efficiency effectively, because it's correlated with the uncertainty and risk of the financial market directly. It's also a crucial variable contained in the security portfolio theory, assets pricing model, arbitrage pricing model and option pricing formula. Therefore, how to describe the dynamic behavior of the financial time series' fluctuation well is always a hot research point in Financial Econometrics.So far, among various volatility models, autoregressive conditional heteroskedastic (ARCH) model and its numerous extensions especially the generalized autoregressive conditional heteroskedastic (GARCH) model have been widely used, because they can capture the heavy-tailed, large kurtosis and volatility clustering characterized by the financial data. However, both ARCH and GARCH model don't take the structural changes of volatility into consideration. The accumulated evidence from empirical research suggests that the contradiction between the high persistence of the conditional volatility indicated by these models and its poor forecasting results may originate from the structural changes of the variance process. It's widely accepted that shifts are common in financial market, which can be attributed to the new economical policy, adjustment of financial regulation or self-development of the market and so on. So it's necessary to model such structural changes of volatility.In order to capture the statistic characters and the shifts in the volatility of financial data, this paper proposes the general regime switching GARCH model with time-varying switching probability of the states based on the idea of Markov-switching model, and then establishes the regime switching GARCH model with mixture of Gaussian distribution, which is used to fit the stochastic errors in the model. Furthermore, these two models are analyzed from the Bayesian prospective with the aid of the data augmentation technique, and parameters are estimated by Markov Chain Monte Carlo simulation realized by the Gibbs sampling. This Bayesian estimation method avoids the path dependence problem in the traditional maximum likelihood estimation effectively. Finally, we implement the empirical research on volatility of China stock market by applying above theoretical results to the return series of Shanghai Stock Exchange (SSE) composite index. The results suggest that there exists structural changes in China stock market and after allowing the parameters to change over time the persistence of volatility indeed declines, meanwhile, the regime switching GARCH model with mixture of Gaussian distribution is superior to the regime switching GARCH model with ordinary normal distribution in capturing extreme events of the data .