股市波动的标度无关性算法及应用研究

Study of scaling and application in stock market fluctuation

标度无关性是广泛存在于自然界系统甚至于经济金融系统可观测量的幂函数关系 ,它揭示了股票市场波动的金融复杂性 .在分析股市波动标度无关性及其非趋势波动分析 DFA算法基础上进行了应用研究 ,( i)将 DFA推广为动态递推算法 ;( ii)对国内若干股价指数进行标度指数实际计算 .结果表明 ,递推 DFA算法与 DFA算法、重标极差 R/S分析方法相比具有计算速度快、内存容量小的优点 ,更能适应股市波动分析的实际需要 .国内股市波动的标度无关性分析表明 ,沪深股市具有持久性 ,在重大金融事件的作用下 。

Scaling 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. On the bases of scaling of stock fluctuation and detrended fluctuation analysis (DFA) the application is researched, empirical scaling exponent of stock market is calculated.(Ⅰ)spread DFA into dynamic recursion algorithm; (Ⅱ) calculate the scaling exponent of the prices of some interior stocks. The conclusion shows that, compared with DFA and R/S (rescaled range analysis) recursion DFA computes faster, has smaller internal storage and it can meet with the real demand of stock fluctuation analysis more well. The scaling analysis of interior stock fluctuation shows that Shanghai stock market and Shenzhen stock market have a lasting characteristic. The influence of big financial event to these two stock markets is lasting.