基于分形插值理论的上证综指的分形特征分析与实证研究

基于迭代函数系统,以及分形插值理论的仿射变换,给出了反映股票价格波动的分形插值图形,并以上证综指收盘价的170个数据为基础,利用Matlab软件和FractalFox软件计算其盒维数,对上证综指的分形特征进行了分析。同时,在大样本数据中选取若干个插值点,使用分形插值方法在Matlab软件上绘制出上证综指的分形插值图形。最后研究了上证综指时间序列曲线和分形插值函数曲线的分形维数与Hurst指数,对上证综指的波动性及长期相关性等特征作了进一步的讨论。

Analysis and Empirical Study on Fractal Feature of Shanghai Composite Index Based on Fractal Interpolation Theory

Based on iterated function system and affine transformation of fractal interpolation theory,the paper gives the fractal interpolation graphics which reflect the volatility of the stock price.By using Matlab software and FractalFox software to calculate the box dimension,the fractal characters of Shanghai composite index are analyzed based on 170 data from closing price.At the same time,choosing several interpolation points from a large sample data,fractal interpolation graphics of Shanghai composite index are drawn in Matlab software using the fractal interpolation method.Finally,by studying on time series curve of Shanghai composite index,fractal dimension on fractal interploation curve and Hurst index,the paper makes a further discussion on the features of Shanghai composite index such as volatility and long-term correlation.