An Empirical Study On Shanghai Composite Index Based On MCMC Estimation Of MS-GARCH Model

With the rapid development of financial markets,financial innovation and economic globalization,the importance of performance attribution analysis and risk management of financial instruments has become more prominent,and both are rely on analysis and modeling of financial data.Time series analysis theory is one of the financial market data analysis tools,and the results often show an impact of unit root when fitting data of return series with classic GARCH model.On this basis,the MS-GARCH model was proposed,on the one hand is used to characterize the structure shifts of boom and bust,or Bull and Bear,on the other hand is used to find out whether the impact of unit root is caused by misuse of model.We select the weekly log return of Shanghai Composite Index as research subjects.Firstly,we choose the suitable model for the data fitting according to the descriptive statistics and hypothetical tests.Then we define the three states which mean up,down and fluctuation according to the plot of closing price and hope to find out through empirical analysis that the differences between fitting results of GARCH model and MS-GARCH model.We choose the Bayesian parameter estimation and MCMC algorithms for MS-GARCH model,and derive the full conditional distributions of posterior under the normal distribution assumption of residuals,so that we can use the Gibbs Sampling for parameter estimation.After that,we use MATLAB for programming,and get 20000 samples under different sets of prior distribution and iteration initial value.By analyzing the results,we find out that the fitting results won't change too much by changing the initial value,but will change a lot due to the different prior distributions.The transition probabilities are also affected by initial setting of states.So we think that the fitting results of MS-GARCH model will reflect the knowledge of researchers,so that the model can be useful when finding proof for a guess.