[1] Wang Haiyan, Zhu Mei,. A prediction comparison between univariateand multivariate chaotic time series [J]. Journal of Southeast University (English Edition), 2003, 19 (4): 414-417. [doi:10.3969/j.issn.1003-7985.2003.04.023]

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A prediction comparison between univariateand multivariate chaotic time series()

混沌时间序列单变量和多变量重构的预测比较

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

19

Issue:

2003 4

Page:

414-417

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2003-12-30

Info

Title:

A prediction comparison between univariateand multivariate chaotic time series

混沌时间序列单变量和多变量重构的预测比较

Author(s):

Wang Haiyan¹, Zhu Mei²

¹College of Economics and Management, Southeast University, Nanjing 210096, China
²Department of Mathematics, Southeast University, Nanjing 210096, China

王海燕¹, 朱梅²

¹东南大学经济管理学院, 南京 210096; ²东南大学数学系, 南京 210096

Keywords:

multivariate chaotic time series;  phase space reconstruction;  prediction;  neural networks

多变量混沌时间序列;  相空间重构;  预测;  神经网络

PACS:

O175;O241

DOI:

10.3969/j.issn.1003-7985.2003.04.023

Abstract:

The methods to determine time delays and embedding dimensions in the phase-space delay reconstruction of multivariate chaotic time series are proposed. Three nonlinear prediction methods of multivariate chaotic time series including local mean prediction, local linear prediction and BP neural networks prediction are considered. The simulation results obtained by the Lorenz system show that no matter what nonlinear prediction method is used, the prediction error of multivariate chaotic time series is much smaller than the prediction error of univariate time series, even if half of the data of univariate time series are used in multivariate time series. The results also verify that methods to determine the time delays and the embedding dimensions are correct from the view of minimizing the prediction error.

提出了多变量混沌时间序列相空间延迟重构中延迟时间间隔和嵌入维数的选取方法, 给出了多变量混沌时间序列的局部平均预测法, 局部线性预测法和BP神经网络预测法等3种非线性预测方法.通过Lorenz系统的仿真计算表明, 无论用3种非线性预测方法中的哪一种, 多变量混沌时间序列要比单变量混沌时间序列的预测误差小得多, 即使前者的数据长度只有后者的一半, 前者的预测误差也要小很多.另外从预测误差最小的角度验证了多变量混沌时间序列相空间延迟重构中延迟时间间隔和嵌入维数选取方法的有效性.

References:

[1] 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.(in Chinese)
[2] Cao Liangyue, Mees A, Judd K. Dynamics from multivariate time series [J]. Physica D, 1998, 121(1, 2):75-88.
[3] Boccaletti S, Valladares D L, Pecora L M, et al. Reconstructing embedding spaces of coupled dynamical systems from multivariate data [J]. Physical Review E, 2002, 65(1):1-4.
[4] Porporato A, Ridolfi L. Multivariate nonlinear prediction of river flows [J]. Journal of Hydrology, 2001, 248(1-4):109-122.
[5] Reick C H, Page B. Time series prediction by multivariate next neighbor methods with application to zooplankton forecasts [J]. Mathematics and Computers in Simulation, 2000, 52(3, 4):289-310.
[6] Kennel M B, Brown R, Abarbanel H D I. Determining embedding dimension for phase space reconstruction using a geometric construction [J]. Physical Review A, 1990, 151(5): 225-233.
[7] Cong Shuang. Neural networks, fuzzy systems and their applications to motion control [M]. Hefei: University of Science and Technology of China Press, 2001. 26-27.(in Chinese)

Memo

Memo:

Biography: Wang Haiyan(1966—), male, doctor, associate professor, hywang@seu.edu.cn.

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