Research Of SSE Composite Index Volatility Based On Markov Switching ARCH Model

As a barometer of economic trends, having developed for more than20years, the stockmarket of China has accumulated a lot of bubble, and shows market volatility to some extent,therefore it is of great significance for measuring and analyzing the feature of volatility. Inthis paper, take the daily yield rate of Composite Index of Shanghai Stock Exchange forexample, the kind of complex financial data based on maximum likelihood estimation methodto draw a simple GARCH family models can not describe the the feature of volatility，likeleptokurtosis, clustering, long memory,leveraged and so on.Therefore, in order to measuring the feature of volatility effectively, this paper attemptsto use R/S analysis, assuming that the residuals are normally distributed, t distribution, GEDdistribution and SKT distribution, use the “rolling time window” approach for volatilityforecast, Make an empirical analysis by using ARFIMA(p,d,q)-EGARCH(m,n)-M model, Theempirical results show that: the yield rate has long memory; Based on SKT distribution,ARFIMA(2,1)-EGARCH(1,1)-M model can better handle series feature, like fattail,clustering and other features, compared to other distributions, this distribution also havemore forecasting precision.Then on the basis of the GARCH model, combined with the state-space model withMarkov switching for extended, the paper discusses the three-state MS-ARCH(3) model,using the MCMC parameter estimation, take the Metropolis-Hasting sampling nested withinGibbs sampling method for sampling parameters. The empirical results show that:MS-ARCH model is better than the GARCH model in terms of performance characteristicsdescribe the volatility clustering, especially can handle the structural break while the GARCHmodel can not do. MS-ARCH advantage is also reflected in practical applications, such as therole of the crisis warning. Besides, recommended inverstors to take the opportunity to profitfrom the high volatility, but when the high volatility state began to gather as a massive,inverstors should be on alert and beware of the loss caused by crisis.