股票市场的分形维数分析  

Analysis of Fractal Dimensions in Stock-market

作　　者：李志勇[1] 王春红[2] 陈良生[2] 朱伟勇[1] 

机构地区：[1]东北大学信息科学与工程学院,辽宁沈阳110004 [2]沈阳大学,辽宁沈阳110044

出　　处：《东北大学学报（自然科学版）》2003年第7期666-669,共4页Journal of Northeastern University(Natural Science)

基　　金：教育部博士学科点专项科研基金资助项目(200014512);国家自然科学基金资助项目(69974008).

摘　　要：针对股票市场所具有的混沌特征,运用分形理论的方法对上证指数进行分析·采用一种构造生成元的新方法尺度生成法构造出上证综合指数的生成元·根据分形迭代函数系统理论与方法,迭代生成上证综合指数的模拟走势图·根据尺度C定义极值总变化函数R(C),从而定义一种新的维数栏维Df,与分形维数、关联维数一起完成对股市波动的复杂程度的定量估计·An extension of extreme values was introduced to generate the constructunit. Using these extreme values determined by a scale, the real trend of the stock market can be found. Using the generated constructunit, the simulate trend picture was made by the theory of IFS(Iterated Function System). On the basis of scale C, the function of total variation R(C) and a new fractal dimension were introduced. The fractal dimension and relation dimension were calculated to describe the complex degree of the stock market. An example was given for the application of the nonlinear model in describing the simulate trend of Shanghai stock market.

关 键 词：股票市场 分形结构 波动 生成元 分形维数 关联维数 

分 类 号：TP301.5[自动化与计算机技术—计算机系统结构]