Fractal And Chaos Theory Applied To China's Stock Market

This paper break the traditional Efficient Market Hypothesis, studying on China's stock market from a new perspective. The tools used are R/S method in nonlinear analysis and nonlinear dynamics research methods of strange attractors in chaos theory. First of all, the basic principles of fractal, Fractal Market Hypothesis, the method of R/S analysis and Hurst index were introduced. We studied the fractal characteristics on the 5th logarithmic yield sequence of the Shanghai 180 Index and the Shenzhen A-share Index by using R/S analysis and V-statistic. The empirical results show that Shanghai and Shenzhen stock markets are random walk process with deviation existing state sustainability and non-periodic cycles. Shenzhen stock price formation system is more complex than the Shanghai market. Meanwhile, it's more difficult for forecasting. Secondly, discuss the basic features of chaotic phenomena, and focus on the two features of the chaotic system—the fractal dimension and the Lyapunov exponent. We study China's stock market by using the technique of phase space reconstruction and get the fractal dimension of attractors. Meanwhile, The largest Lyapunov exponent is positive. This shows that China's stock market is a complex dynamic system with the characteristics of chaotic systems. Finally, nonlinear cointegration theory is used to study the nonlinear balanced relationship between return of assets and impact factors. The dissertation gives out the three-factor CAPM under Fractal Market Hypothesis. We use wavelet neural network to construct the nonlinear cointegration function.