Scale Theory and Empirical Research in the Securities Market
证券市场的标度理论及实证研究

Scaling invariance is found in a wide range of systems from nature to society, of economy and finance, is the power law behavior of a particular observable, financial complexity is promulgated. Applying fractal theory, we approach self-similar and scale invariance of securities market and analyze three kinds of scale index i.e autocorrelation index, Hurst index, on the basis of scale index of DFA calculation method. We improve Hurst index. Based on time series standard deviation. DFA is spreaded into dynamic recursion algorithm. Using three kinds of scale index, we conduct empirical research on internal Shenzhen Shanghai stock market. The result indicates that the profit rate of Shanghai Shenzhen markets all does not obey normal distribution. Correlation exists between the index of the stock price in stried over the time scales. It expresses the fractal time series. It indicates that the policy guide hidden at the back influences this character of China stock market.