Market Efficiency And Nonlinear Statistical Analysis On Shanghai Composite Index

Effective Market Hypothesis has always been an important part of the financial economics, and we can find it in Markowitz portfolio selection theory, the capital asset pricing theory, arbitrage pricing theory, and the option pricing theory. At the same time, the relative effectiveness level of a market also reflects the maturity of the market and the rationality of market participants. The stock market of our country has been established for 25 years as yet, and the economic status of the stock market is becoming more’ and more important So it is very necessary to have a research on the effectiveness of the China stock marketIn this paper we firstly have a brief introduction of the theoretical connotation of the EMH, introduce the classification and the empirical test model of the EMH. Secondly, we elaborate the unit root test, Ljung-Box correlation test, variance ratio test and BDS test in the view of statistics which are related to the three forms of random walk model. Thirdly, we use the method introduced in the previous to test the day closing price logarithmic sequence of Shanghai composite index from 1992 to 2014, and we separate the data into three intervals, namely 1992-1997,1998-2006 and 2007-2014. And the test results show that the Chinese stock market return sequence are stationary series, but they didn’t pass the correlation test, variance ratio test and BDS test So there exists correlation in the return sequence, the stock market has not yet to reach weak form efficient Finally, in order to identify the nonlinear correlation structure of the return sequence, we set up the ARMA model to eliminate the linear correlation of original return sequence, and test the nonlinear correlation of the model’s residual sequences by means of BDS test And we know that the nonlinear structure is multiplicative structure through the Hsieh-third order moment test At the same time, we establish the ARMA-GARCH model to describe the multiplicative structure of the original return sequence, and evaluate the model by using the last month’s data of each period.