Empirical And Application Study Of Non-linear Theory In China's Stock Market

This thesis comes from the project: 'A Research on the Chaos and Fractal in China Stock Market', which is funded by ministry of education.Efficient Market Hypothesis is the foundation of a series of modern classic theories in finance, and it has been applied widely on the research in the capital market. However, with the development of non-linear theories and the appearance of many abnormities in the market, people have begun to realize the limitation and the failure of linear theories, and non-linear theories and methods have become the leading actor. This paper begins with the EMH and its traditional test methods. According to strict logicality, we find out the limitation of old test methods and only non-linear analytical method can study the capital market. Furthermore the results of the empirical study reveal that the realistic situation is contrary to EMH and China's stock market is a non-linear dynamical system and possesses remarkable Chaos and Fractal characteristics. This discovery will help us to understand the stock market of China with new point of view, and guide us to grasp the rules of the market better.This paper includes four chapters.The first chapter-the linear theories in stock market and the invalidation. Onthe one hand, the author introduces the foundation of the capital market theory -Efficient market hypothesis and some other classical linear models that are based on it; on the other hand, the author uses the traditional methods such as the run test, the autocorrelation coefficients test and the ADF test to test the weak form of EMH with real data in China's stock market. Finally this chapter analyses some abnormal phenomena contrary to EMH in the stock market. From the results, the author puts forward that non-linear theories and methods should be used to study the capital market.The second chapter-the current research of the non-linear theories in thestock market. This chapter summarizes and introduces two major important fields innon-linear theories: the Chaos and Fractal theory, and summarizes some current researches about them home and abroad.The third chapter-the empirical research on the non-linear theories in China'sstock market. This chapter tests whether the non-linearity exists in China's stock market by normal distribution test, GARCH effect test, long-term memory test, etc. And it calculate the Lyapunov exponent and the fractal dimension, which indicate that EMH is not conform to reality market, and China's stock market is a non-linear dynamical system and possesses remarkable Chaos and Fractal features.The fourth chapter-the application study of the non-linear theories in China'sstock market. This chapter pays close attention to two major applications in non-linear theories: Fractal market hypothesis and applications in portfolio models. At last, whether Levy distribution can be used for describe the distribution of stock returns in China is discussed.The innovative work of the thesis: (1)adopt systematical and complex methods and a theoretical frame with qualitative and quantitative analyses to investigate complicated problems in capital market.(2)adopt some test methods and intelligent programs such as GARCH , RBF, and use various empirical analyses based on computer simulation to understand the complexity of the capital market.(3)propose the portfolio optimization model based on non-normal distribution, (4)discuss the problem whether Levy distribution can describe the distribution of returns of stock prices in China's stock market.