A Research On The Volatility Of The Chinese Stock Market Based On The GJR-GARCH Model Of The State Transition

Among the traditional models of volatility,the GARCH model can describe the characteristics of the financial time series in a good way,such as the fat tail and volatility clustering.However,when the financial time series exists a structural change,Neither the GARCH model nor the asymmetric GARCH model,can accurately depict the volatility of the data.This problem can be solved effectively by introducing Markov state switching into the GARCH model.This paper will establish a MRS-GJR-GARCH model to the study the fluctuation problem of Chinese stock market.The first chapter describes the background and significance of this paper,and summarizes the domestic and foreign literature.The second chapter summarizes the forms of the GARCH models and the description of characteristic for the data,they consist of GARCH,EGARCH and GJR-GARCH model and the Markov state switching GJR-GARCH model.The third chapter carries on the data selection and the characteristic test,which is based on the structure of model.At first,the paper selects the daily closing price of CSI 300 from April 8th,2005 to August 28th,2015,calculating Logarithmic return rate as the research object;secondly,the basic statistical characteristics of the data is described and analyzed;finally,the data are operating by stationary test,the ARCH effect test,the nonlinear test and the structural transformation test.The various results of analysis and tests show that the selected sample data have the characteristics of volatility clustering,fat tail,stationary,non linearity and structural switching.The fourth chapter researches the volatility on the stock market by GARCH models based on the single state.First,according to the examination result of data from the third chapter,we set the the different forms of GARCH model;then,the GARCH(1,1),EGARCH(1,1)and GJR-GARCH(1,1)model are estimated by the traditional maximum likelihood estimation method which the error terms satisfied normal distribution,t distribution and generalized error distribution;calculating the result finally.By comparing the AIC,SC information criterion and log likelihood statistics,the error terms satisfied generalized error distribution is the most appropriate model,which can reflect the spike and fat tail of characteristics for the rate of return,but the three models can not be effectively characterized the highly volatility and non symmetry.The fifth chapter studies the volatility based on the MRS-GJR-GARCH model.First,according to the result of the study in the fourth chapter,we select the error terms satisfied generalized error distribution;by introducing the Markov state switching model into the GJR-GARCH model,we establish the two state MRS-GJR-GARCH model,and choosing the MCMC method to estimate the parameters;at last,the two states MRS-GJR-GARCH model are analyzed in detail,comparing the single GARCH model based on MCMC method.The result shows the former can reduce the high volatility occurred by ignored state switching and gain lever effect between two states.The lever effect indicates stronger influence in high volatility state.Through the results of the model estimation,we can get the expected return rate,unconditional variance and duration under different states from the Chinese stock market.The sixth chapter summarizes the conclusions and prospect of this paper.