Chaotic And Multi-fractal Character Analysis In Chinese Stock Market

The classic capital market theories makes the simplistic assumptions to the capital market, using the linear model to describe the capital market, because linear model makes them easy to handle and the influence of the reductionist in classic Physics. Simplistic assumption is jeopardizing and the theoretical result can't explain practical problems usually. Efficient Market Hypothesis (EMH) is the sill of the classic capital market theories. It assumes that investors are rational, the securities market is informationally efficient, market prices reflect all public information available and all prices are "fair". Consequently, security returns (price change) follow a random walk, and volatility in financial market is the result of exogenous stochastic events (white noise). But lots of phenomena on the capital market can't explain with the EMH, such as high peak and fat tail in security returns, the sudden collapse in stock market and long-memory in stock series.Researchers and risk managers can gain a new perspective by the developing of the complexity theories. Based on the complexity theories, this paper uses the tool of chaos and fractal to analyze the structure of Chinese stock market. From those experiments, one can conclude that Chinese stock market returns series follow a biased random process, and exhibit fractal characteristic and long-memory effect. Chinese stock market returns series have multi-fractal characteristics, and the multi-fractal characteristics of ShengZhen synthesis stock price index(SZSSPI) is more obviously than ShangHai synthesis stock price index(SHSSPI).Through BDS test, it can be seen that the logarithmic price increments of SHSSPI are not totally at random, which contradicts effective market hypothesis. The rejection of the white noise process indicates that the Shanghai stock market is not the weak effective market, the non-linear correlation structure existing among them.Through calculating the fractional dimension, the correlation dimension of logarithmic price increments of SHSSPI is among 2.5-2.7, and evolving till final stage systematically, correlation dimension value is constringed in 2.6. This means that the price movement model of this system can be set up with three dynamic variables.