Markov Regime-Switching GARCH Model And It's Application In Data Analysis Of China's Stock Market

Robert Engle(1982) proposed the autoregressive conditional heteroscedasticity(ARCH)model to describe the volatility of financial time series. Based on Engle's work, Bollerslev(1986) built the general autoregressive conditional heteroscedasticity(GARCH) model. The GARCH model and it's extensive forms have been widely applied to economic and financial time series. In practice macroeconomic policy adjustments or the stage of the economic cycle may be change the coefficients of the mathematical model. Markov switching-regime(MS)model is one of the most important models to capture this coefficients change. This paper mainly studied Markov switching-regime GARCH(MS-GARCH) model and it's application in data analysis of China's stock market. So this research has some values both on theory and practice.In this paper, we first introduce some basic knowledge, such as EM algorithm, the two step estimation of GARCH model, MS model. Then we recall a MS-GARCH model that incorporates the features of both Markov switching-regime model and GARCH model. Estimating this model is a challenging task, because not only parameters and Markov transition probabilities are needed to be estimated, but also the inference about the value of the regime has to be done based on the samples. So this article provide a novel approach based on EM algorithm and the two step estimation of GARCH model, the algorithm and steps of estimation and inference are given in details.In the empirical analysis we analyze the return rate of data of Shanghai Composite Index,the sampling data from January 4, 2006 to December 31, 2015. The results show that, firstly,there are volatility clustering and 3 regime switching features in the selected samples. Secondly,MS-GARCH model can describe return rate series better than that of other models. Thirdly, Our algorithm of MLE method of parameters of MS-GARCH model is effective.