MCMC Estimation And Analysis Of Markov Switching-GARCH Model

Financial data have important statistical features like fat tail, volatility clustering and leverage effects, which could be characterized by ARCH model, GARCH model and derived GARH model. However, with the ever changing global economy and financial markets, financial time series may exhibit volatility and the financial market may has structural abruptness. So it is necessary to model the ever changing structure of volatility. Because of single structure and constant parameters, traditional GARCH model can not reflect the structural changes and the description and prediction of fluctuations is not accurate enough. Hamilton proposed Markov-Switching model(MS model), which provides new ideas and methods to solve this problem.In order to accurately describe the prevailing structural abruptness in financial time series volatility, we introduce Markov state transition model on the basis of single state GARCH model, and establish Markov-Switching GARCH model,. This new model divide volatility into two states: high and low, corresponding to GARCH model with different parameter structure. The transfer of state is subjected to Markov process. However, due to the path dependence issue, maximum likelihood estimation is not feasible. We start from Bayesian method, use MCMC(Markov chain Monte Carlo) simulation with Gibbs sampling to estimate the model parameter and avoid the path dependence issue effectively. In this article, the empirical analysis is based on Shanghai Composite Index and the result shows that China’s stock market volatility exists structural change. MS-GARCH model of two states is better than GARCH model of a single state: the former not only capture the volatility characteristics of the stock better, but also reflects the law of market development.