Change Structure Analysis Of The Stock Market Index Rate Of Returns

Change point problem is a very important research area in statistics, which is extensive used in finance and meteorological. For a column of data, if it’s mean, variance or the parameters of distribution that the data obeyed is changed, we can say that, there is a change point in the data. The time of the change happens is called as the change point. In financial area, especially in stock market, change point problem mainly consider the returns of the stock markets. In this paper, we use the daily returns’ value at risk (VaR) and the successive raises and falls of returns to study the change point problem. The paper is organized as follows.In Section 1, we introduce the history and the use of the change point study. Then we talk about the study history and research status of the financial crisis and financial contagion. At last we study some theory about the successive raises and falls or returns.In Section 2, we mainly introduce the theory of the quantile-VaR and the expectile-VaR which is used in change study with financial contagion. And then we introduce some theory with Box-Cox change and penalized maximal F test (PMF).In Section 3, we do the empirical analysis of the financial contagion. We choose the daily returns of the economic index of China, U.S.A, U.K, German, Japan and Hongkong from 2006 to 2012. We make linear Expectile model to consider the changes between USA and others. We analysis the parameters of the linear model to find the change point and compare the parameters’ change before and after the change point happen. Combination with the real situation, we explain the result reasonable.In Section 4, we consider the daily returns of Chinese SSE Composite Index from 2000 to 2014. We use TransPMF test to study the position of the change point in the successive raises and falls of returns.In Section 5, we summary the change point study we used in this paper.