[1]王海燕,盛昭瀚,张进.多变量时间序列复杂系统的相空间重构[J].东南大学学报(自然科学版),2003,33(1):115-118.[doi:10.3969/j.issn.1001-0505.2003.01.029]
 Wang Haiyan,Sheng Zhaohan,Zhang Jin.Phase space reconstruction of complex systems based on multivariate time series[J].Journal of Southeast University (Natural Science Edition),2003,33(1):115-118.[doi:10.3969/j.issn.1001-0505.2003.01.029]
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多变量时间序列复杂系统的相空间重构()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
33
期数:
2003年第1期
页码:
115-118
栏目:
数学、物理学、力学
出版日期:
2003-01-20

文章信息/Info

Title:
Phase space reconstruction of complex systems based on multivariate time series
作者:
王海燕1 盛昭瀚2 张进3
1 东南大学经济管理学院,南京 210096; 2 南京大学管理科学与工程研究院,南京 210093; 3 南京审计学院金融系,南京 210029
Author(s):
Wang Haiyan1 Sheng Zhaohan2 Zhang Jin3
1 College of Economics and Management, Southeast University, Nanjing 210096, China
2 Graduate School of Management Science and Engineering, Nanjing University, Nanjing 210093, China
3 Department of Finance, Nanjing
关键词:
复杂系统 多变量时间序列 相空间重构 广义关联维数
Keywords:
complex systems multivariate time series phase space reconstruction generalized correlation dimensions
分类号:
O175;O241
DOI:
10.3969/j.issn.1001-0505.2003.01.029
摘要:
根据单变量时间序列相空间重构思想,提出了多变量时间序列描述的复杂系统的相空间延迟重构方法.对每一分量的时间序列,分别利用互信息最小法确定最佳延迟时间间隔,最小嵌入维数的选取方法是单变量时间序列情况下虚假邻点法的推广.给出了q阶广义关联积分和q阶广义关联维数的计算公式,并证明了广义关联维数与所用范数无关.计算了Lorenz系统按前2个变量进行重构时的最佳延迟时间间隔和最小嵌入维数.计算结果表明,用多变量时间序列重构比用单变量时间序列重构所需的数据长度要短得多且在方法上更有效.
Abstract:
According to the phase space reconstruction of a single variate time series, a new phase space delay reconstruction method based on multivariate time series of complex systems is proposed. The good time delay is chosen for each scalar time series by mutual information. The method to get the minimum embedding dimension by the false neighbor in single variate case is popularized to multivariate case. The formulation of generalized correlation integration and generalized correlation dimension of order q are proposed, which are not influenced by norm. Simulated by the Lorenz system with the first two variates, the good time delay, the minimum embedding dimension and the generalized correlation dimensions of order 1,2,3 are calculated. The results confirm that the length of the time series is shorter and the method is more efficient in reconstruction based on multivariate time series than single variate time series.

参考文献/References:

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备注/Memo

备注/Memo:
作者简介: 王海燕(1966—),男,博士,副教授.
更新日期/Last Update: 2003-01-20