Research On Change-points In Shanghai Composite Index: Based On Structure Mutation AR(p) Model With Lag Coefficient Mutation

As an emerging market, China’s stock market is vulnerable to the influence ofexternal factors and presents large fluctuations as a result of all kinds of reasons, suchas imperfection in legal construction and market operating mechanism,psychologically immaturity of investors. Therefore, structural mutations are morelikely to occur in China’s stock market. However, there are still few detailed andsystematic researches on change point of China’s stock market. Thus, to study thestructure change of China’s stock market and to explore the main reasons leading tostructural mutations has an important theoretical and practical significance for China’sfinancial risk management and policy formulation.Firstly, this article summarizes the empirical researches at home and abroad onthe structural mutation detection methods and structure mutations of stock index. Onthis basis and in the framework of Bayesian theory of econometrics, this article forthe first time introduce the binomial distribution to AR(p) model with structurechange in its lag coefficients, considering the mean mutation and variance mutation,and comprehensively analyze the mutations of the time trend, intercept, lagcoefficient and variance. Based on Bayesian theory, this paper constructs likelihoodfunction, and at the same time introduces the hierarchical prior distribution by using apriori information and sample information. Then this article uses Gibbs sampling andMH algorithm to complete the judgment of change point number and location.Furthermore, in order to analyze the structure change of China’s stock index, thisarticle selects Shanghai Composite Index as the research object. Then, based on AR(p)model with structure change in its lag coefficients, this paper analyzes the structurechange point of the Shanghai index. The results showed that in May1992to April2012, the Shanghai index had14structural breaks:4mean-variance change points,1mean change point, and9variance change points. After that, the paper detailedlyanalyzes the reasons for mean-variance change points. It founds that, the ShanghaiComposite Index has mean-variance change points, largely because of the macroeconomic situation at home and abroad. At the same time, this model compareswith the structural mutations AR(p) model that its lag coefficient is constant forShanghai index, and the results is that in structure mutation of Shanghai index, AR(p)model with structure change in its lag coefficients is more effective.Finally, conclusions and policy recommendations of this paper are that, China’sstock market has a significant cyclical, it can be divided into high-speed down stage,slowly down stage and up stage. The government has carried out bailout operationsrepeatedly, most of which failed to meet the target to change the trend of stock priceindex running in the long term. In order to maintain a healthy and rapid developmentof the domestic stock market, the state should vigorously develop the domesticeconomy, maintain steady and rapid economic development, create a favorableeconomic environment, and further improve the various systems of the domesticstock market.