基于灰色算子的分形法及应用

doi:10.16381/j.cnki.issn1003-207x.2017.10.010

中国管理科学 ›› 2017, Vol. 25 ›› Issue (10): 89-99.doi: 10.16381/j.cnki.issn1003-207x.2017.10.010

基于灰色算子的分形法及应用

周伟杰¹, 党耀国², 顾荣宝³

1. 常州大学商学院, 江苏常州 213164;
2. 南京航天航空大学经济与管理学院, 江苏南京 211106;
3. 南京财经大学金融学院, 江苏南京 210046

收稿日期:2014-05-22 修回日期:2017-07-10 出版日期:2017-10-20 发布日期:2017-12-15
通讯作者: 周伟杰(1983-),男(汉族),江苏常州人,常州大学商学院,讲师,研究方向:灰色系统、金融工程,E-mail:wjzhou@cczu.edu.cn. E-mail:wjzhou@cczu.edu.cn
基金资助:
国家自然科学基金资助项目（71701024）

The Modified Fractal Methods Based on the Grey Operator and Their Application

ZHOU Wei-jie¹, DANG Yao-guo², GU Rong-bao³

1. Business College, Changzhou University, Changzhou, 213164, China;
2. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;
3. School of Finance, Nanjing University of Finance and Economics Nanjing 210046, China

Received:2014-05-22 Revised:2017-07-10 Online:2017-10-20 Published:2017-12-15

摘要/Abstract

摘要： 在灰色缓冲算子和灰色调整系数的框架下，构造灰色算子，提出了权重可调的加权移动平均去趋势法，进一步将其拓广为多重分形加权移动平均去趋势法。算法表明原有的移动平均去趋势法及其多重分形形式分别是加权移动平均去趋势法及其多重分形的特例。用带波动和线性趋势的分形高斯噪声与二项式多重分形进行数值模拟，表明权重为6的中心加权移动平均去趋势法及其多重分形能有效地去除序列趋势，计算出的Hurst值和多重分形谱f（α）比原有算法更接近真值。将权重为6的中心加权移动平均去趋势法及其多重分形分析南京市气温序列的长记忆性与多重分形性，结果表明从1951-2008年，七月份气温增速要明显小于一月份的增速，一月份和七月份气温都存在长记忆性，但七月份气温序列的长记忆性要高于一月份，表明一月份和七月份气温序列均可预测，七月份的可预测性更高些，这为通过预测对气温灾害风险防范提供了可行性；此外，一月份、七月份的气温序列均有多重分形性，说明可从多标度角度对其建模分析。

关键词: 灰色算子, 加权移动平均去趋势法, 多重分形加权移动平均去趋势法, 长记忆性

Abstract: Under the framework of grey buffer operator and grey adjustment coefficients, the grey operation is constructed, and the weighted detrended moving average with adjustable weighted coefficients and its multifractal form called as multifractal weighted detrended moving average are put forward. The original detrended moving average is a special of the modified fractal method. Numerical simulation on fractal Gauss noise and binomial multifractal with fluctuation and linear trend shows that the centered detrended weighted moving algorithm whose weight is 6 can effectively remove the sequence trend, and the accuracy of Hurst and f(α) calculated by weighted detrended moving average and multifractal weighted detrended moving average are more close to analytics value compared with original algorithm. In empirical part, the long term memory and multifractality of daily temperature series in Nanjing from 1951 to 2008 by modified methods are investigated. The results show that the growth rate of temperature in July is significantly smaller than that of January; compared to the original methods, the conclusions from modified fractal methods are more close to reality; all temperature sequences have the long term memory feature, but the long term memory of daily temperature series in contained the highest, the lowest and the average temperature are stronger than that in January, which indicates that predictability of temperature in July is higher than that in January. The prediction of temperature series gives a way to manage the temperature disaster risk. Besides, temperature series of Nanjing in January and July possess multifractality, which suggest that the temperature series can be studied from multi scale. Through the shape of multifractal spectrum, it is found that the internal structure of the highest and average temperature sequences are more complex than the lowest temperature sequences whether for January or July.

Key words: grey operator, weighted detrended moving average, multifractal weighted detrended moving average, long memory

中图分类号:

C931

周伟杰, 党耀国, 顾荣宝. 基于灰色算子的分形法及应用[J]. 中国管理科学, 2017, 25(10): 89-99.

ZHOU Wei-jie, DANG Yao-guo, GU Rong-bao. The Modified Fractal Methods Based on the Grey Operator and Their Application[J]. Chinese Journal of Management Science, 2017, 25(10): 89-99.

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基于灰色算子的分形法及应用

The Modified Fractal Methods Based on the Grey Operator and Their Application

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