时间序列曲线盒维数的一种快速算法  

A Fast Algorithm for Determining the Box-counting Dimension of Time Series Trace

作　　者：王炳雪[1] 史忠科[1] 吴方向[1] 

机构地区：[1]西北工业大学自控系,西安710072

出　　处：《系统工程》2000年第4期68-72,共5页Systems Engineering

摘　　要：盒维数是应用最为广泛的维数之一 ,它在信息处理、预测等领域都有成功的应用。目前 ,对盒维数的计算主要采用网格法 ,但该算法需处理分形集合在网格中的计数问题 ,所以计算机处理起来很不方便。针对一维时间序列 ,提出了在不同间隔时间内寻求最大离差的方法 ,避免了集合的计数问题。应用该算法对上证指数的时间序列曲线的盒维数的计算表明上证指数存在着长程正相关。Box counting Dimension is frequently used in fractal analysis and has been successfully used in information processing,forecasting and many other field.Now,the basic algorithm for determining box counting dimension is the gridding method.But the algorithm need count the numbers of square boxes covered by the fractal set and the job is not easy for a computer.Here a fast algorithm for determining the box counting dimension is proposed,which calculates the maximum dispersion of time series points of certain ranges instead of counting square boxes.Based the fast Algorithm,the box counting Dimension of stock aggregative index time series on Shanghai Stock Exchange is calculated and the result shows the aggregative indextime series is long correlative.The result of computer simulation on a trace of Wiener process also shows that the proposed algorithm is feasible and effective.

关 键 词：分形 盒维数 时间序列 快速算法 

分 类 号：O211.61[理学—概率论与数理统计]