证券市场的标度理论及实证研究

运用分形理论探讨证券市场的自相似性与标度不变性 ,分析三种标度指数 ,即自相关指数、Hurst指数、基于 DFA算法的标度指数 .基于标准差时间序列改进 Hurst指数 ,将 DFA推广为动态递推算法 .利用三种标度指数对国内沪深股市进行实证研究 .结果表明 ,沪深股市收益率均不服从正态分布 ,在跨时间尺度的股价指数之间存在着相关性 ,表现为分形时间序列 ,说明其背后所隐含的政策导向影响中国股票市场的特征 .

Scale Theory and Empirical Research in the Securities Market

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.