配分函数法的改进及应用

周伟杰, 党耀国, 顾荣宝, 林晨昱

系统工程理论与实践 ›› 2014, Vol. 34 ›› Issue (3) : 668-675.

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系统工程理论与实践 ›› 2014, Vol. 34 ›› Issue (3) : 668-675. DOI: 10.12011/1000-6788(2014)3-668
研究论文

配分函数法的改进及应用

    周伟杰1, 党耀国1, 顾荣宝2, 林晨昱1
作者信息 +

The modified partition function method and its application

    ZHOU Wei-jie1, DANG Yao-guo1, GU Rong-bao2, LIN Chen-yu1
Author information +
文章历史 +

摘要

针对传统配分函数难以处理分割子区间长度s不为时间序列长度T的约数或者T为质数的情况,采用类似多重分形去趋势波动法(MFDFA)的操作方式,提出修正配分函数法. 用二项式多重分形做数值模拟,得出的数值解与理论值几乎重合,表明修正配分函数法是有效的. 并较为详细地给出了配分函数法各参数的经济含义. 用修正配分函数法分析了上证A股指数的多重分形性,通过打乱序列、去极值、迭代振幅匹配傅里叶变换(IAAFT)研究了多重分形产生的原因. 结果表明:上证A股的分布、极值、序列的时变相关性均影响多重分形的形成,其中序列自相关性为主要因素.

Abstract

On account of traditional partition function hardly applying to the condition that the time series length T is a prime number or cannot be divisible by scaling s, we put forward a modified partition function whose algorithm procedure is similar to MFDFA. Using the numerical simulation of binomial multifractality, the result shows that the new method dealing with the multifractality of time series whose length is prime number is feasible and effective. The economic meaning of parameters in partition function are also discussed. By applying modified partition function, we investigate the multifractality of Shanghai A-share index. Through shuffling, removing extreme values and iterating amplitude adjusted fourier transform technological, we find that the temporal correlation, fat-tail distribution and extreme events are all contributed to the multifractality, but the autocorrelation in sequence plays an important role in the source of multifractality.

关键词

修正配分函数法 / 数值模拟 / 多重分形

Key words

modified partition function method / numerical simulation / multifractality

引用本文

导出引用
周伟杰 , 党耀国 , 顾荣宝 , 林晨昱. 配分函数法的改进及应用. 系统工程理论与实践, 2014, 34(3): 668-675 https://doi.org/10.12011/1000-6788(2014)3-668
ZHOU Wei-jie , DANG Yao-guo , GU Rong-bao , LIN Chen-yu. The modified partition function method and its application. Systems Engineering - Theory & Practice, 2014, 34(3): 668-675 https://doi.org/10.12011/1000-6788(2014)3-668
中图分类号: F830.9   

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基金

国家自然科学基金(71071077,71371098);中央高校基本科研业务费专项资金(NC2012001);江苏省高校哲学社会科学重点研究基地重大项目(2012JDXM005)
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