Chaos, Fractal, And The Stock Market

With the development and growth of the Chinese capital market, the consummating and advancement to the theories of capital market is highly required. Efficient Market Hypotheses and Random Walk Hypotheses are bases of modern capital market theory. However, securities market doesn't obey normal distribution, it shows local random and whole deterministic, which are the chaotic characters of nonlinear system. Securities system is chaotic. Modern capital theory was impacted immensely. So it's an inevitable selection to study capital market in nonlinear ways instead. In this dissertation, this article use nonlinear theory to study our stock market in order to establish new capital theory in our stock markets, which help investors make decision.The results and innovation of the dissertation are in several perspectives:(l)We comparatively analyze EMH and FMH, and analyze the efficient of our stock markets, and conclude that our markets don't obey Efficient Market Hypotheses. So traditional linear theory can't describe our markets, and it's a new direction which chaos and fractal of the nonlinear theory is used to study our markets.(2)We make a systematic analysis on the features of the chaos and fractal in the stock markets. The dissertation studies complex chaotic characteristics, including the circulation of our markets and numerous quantitative indexes of the chaos. By means of the comparison of the quantitative indexes of the chaos, we draw a conclusion that our national stock market is more complex than the one abroad. Moreover, the stock market is extremely sensitive to the original conditions, which is related to the strong fluctuation on stock market. The dissertation presents two quantitative indexes of the fractal characteristics of the stock market: fractal dimension and Hurst exponent. We then draw the conclusion that the functioning system of the stock market will eventually be near the attractor determined by four variations. The important conclusion that our national stock market is characteristic of permanence further proves the irrationality of EMH. The dissertation also analyses the concrete reasons for the fluctuation of our national stock market and proposes reasonable suggestions.(3)This dissertation adopts the partial linear method to predict the Shanghai stock market exponent which is in comparison with the equilibrium prediction. Thus we draw the conclusion that the partial linear prediction model is superior to the equilibrium model. This dissertation finally analyzes the standards and the flaws of the traditional risk measure, claiming that Hurst exponent can take the place of square error to function as the standard for measuring the risk of stock investment. The positive analysis of this claim is also presented in this dissertation.