[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()

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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

Author(s):

Wang Haiyan¹;  Zhu Mei²

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

Keywords:

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

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.

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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