The Empirical Research On Fluctuation Of Shanghai Stock Index Based On The MCMC Method

At present, the stock markets were established late in China, which were a few of the emerging stock markets, and the stock markets were very mature in the developed country. There were lots of different places which affected the fluctuation of the domestic stock markets, so it was very important to research the volatility of the domestic stock markets. It was mainly based on the maximum likelihood theory to optimize the model, when estimating the parameters in the traditional GARCH model. But there were some limitations to the parameters of the GARCH model, it was very difficult to estimate effectively the parameters of the GARCH model, and it existed deviations when estimating the parameters, so it was hard to achieve realizing the optimized objective.In order to solve the above problem effectively in this dissertation, it attempted to apply the theory of Marco Monte Carlo (MCMC) method based on Bayesian to build GARCH model, to describe the volatility of the Shanghai stock index returns time series. This dissertation studied the estimation method of GARCH model from a different point of view, to explore the new field of Bayesian statistics, and improve the model in appropriate. Specifically, this dissertation was applied MCMC method based on the normal distribution in GARCH(1,1) model to estimate parameters, by constructing a converge to the posterior distribution of the parameters to be estimated, thus bypassing constraints from parameters of the GARCH model, to solve difficulties from applying a general optimization method.This dissertation was compared comprehensively empirical research of GARCH model based on BHHH method with that of GARCH model based on MCMC method in the Shanghai stock index fluctuation, trying to make better use of model to describe and explain the volatility of the stock market, it was significant to promote the Bayesian analysis method applying in practice. With the combination of theory and practice, it explored the study of the model theoretical, and also conducted an empirical analysis. In the end of this dissertation, it summarized the result of the research, and prospected research work in the future.