Research on change-points in Shanghai composite index based on AR(p) model with mean and variance structural breaks

As the result of legal construction, market trading mechanism, transaction body,investor psychology immature and other reasons, China stock market, as an emerging market is vulnerable to the influence of external factors and presents large fluctuations. In the framework of Bayesian theory of econometrics, this article for the first time introduced the binomial distribution to AR (p) model with structure change in its lag coefficients, considering the mean mutation and variance mutation, and comprehensively analyzed the mutations of the time trend, intercept,lag coefficient and variance. Based on Bayesian theory, this paper constructed likelihood function, and at the same time introduced the hierarchical prior distribution by using a priori information and sample information. Then we used Gibbs sampling and MH algorithm to complete the judgment of change point number and location. After introducing the method, this paper discussed the structure change point of the Shanghai index. The results showed that in May 1992 to April 2012, the Shanghai index had 14 structural breaks:4 mean-variance change points, 1 mean change point, 9 variance change points.