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非線性時間序列的替代數(shù)據(jù)檢驗方法研究

雷敏,  王志中

雷敏, 王志中. 非線性時間序列的替代數(shù)據(jù)檢驗方法研究[J]. 電子與信息學報, 2001, 23(3): 248-254.
引用本文: 雷敏, 王志中. 非線性時間序列的替代數(shù)據(jù)檢驗方法研究[J]. 電子與信息學報, 2001, 23(3): 248-254.
Lei Min, Wang Zhizhong . Study of the Surrogate Data Method for Nonlinearity of Time Series[J]. Journal of Electronics & Information Technology, 2001, 23(3): 248-254.
Citation: Lei Min, Wang Zhizhong . Study of the Surrogate Data Method for Nonlinearity of Time Series[J]. Journal of Electronics & Information Technology, 2001, 23(3): 248-254.

非線性時間序列的替代數(shù)據(jù)檢驗方法研究

Study of the Surrogate Data Method for Nonlinearity of Time Series

  • 摘要: 目前,替代數(shù)據(jù)方法已逐漸成為時間序列的非線性成分檢驗中廣為采用的一種方法。但對于具有同原始數(shù)據(jù)的均值和方差的線性相關(guān)高斯過程的零假設,通常產(chǎn)生相應替代數(shù)據(jù)的FT(FourierTransform)算法不能很好地重構(gòu)原始數(shù)據(jù)的Fourier頻譜。本文對替代數(shù)據(jù)方法進行了研究,提出了一種改進的FT算法,使得替代數(shù)據(jù)既具有原始數(shù)據(jù)的均值和方差,又具有原始數(shù)據(jù)的Fourier頻譜。利用Gauss數(shù)據(jù)和logistic方程產(chǎn)生的混沌時間序列數(shù)據(jù),證明本文提出的改進算法是可行的,所產(chǎn)生的替代數(shù)據(jù)是合適的。
    Abstract: Currently, the surrogate data method has become a widely used method in testing nonlinearity of time series. However, for the null hypothesis of linearly autocorrelated Gaussian noise with the mean and variance of the raw data, the exiting FT algorithms of generating surrogate data can not reproduce pure frequencies very well. In this paper, the surrogate data method is studied and an improved FT algorithms is proposed. Using the proposed algorithm, the surrogate data sets have the same mean, variance and Fourier spectrum with the original data. This FT algorithm is compared to the previous and proved feasible by using Guass series and chaos time series of the logistic system.
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  • K. Vibe, J. M. Vesin, On chaos detection methods, International Journal of Bifurcation and Chaos, 1996, 6(3), 529-543.[2]J. Theiler, S. Eubank, A. Longtin, et al., Testing for nonlinearity in time series, the method of surrogate data.[J]. Physica D.1992,58:77-[3]C. Poon, C. K. Merrill, Decrease of cardiac chaos in congestive heart failure, Nature, 1997,389(10), 492-495.[4]M. Barahona, C. Poon, Detection of nonlinear dynamics in short, noisy time series, Nature, 1996,381(5), 215-217.[5]U. Parlitz, L. Kocarev, Using surrogate data analysis for unmasking chaotic communication systems, International Journal of Bifurcation and Chaos, 1997, 7(2), 407-413.[6]D. Prichard, J. Theiler, Generating surrogate data for time series with several simultaneously measured variables, Phys. Rev. Lett., 1994, 73(7), 951-954.[7]J. Theiler, D. Prichard, Constrained-realization Monte-Carlo method for hypothesis testing.[J]. Physica D.1996,94:221-[8]T. Schreiber, A. Schmitz, Improved surrogate data for nonlinearity tests, Phys. Rev. Lett., 1996,77(4), 635-638.[9]J.A. Scheinkman, B. Lebaron, Nonlinear dynamics and stock returns, Journal of Business, 1989,62(3), 311-337.[10]J.L. Breeden, N. H. Packard, Nonlinear analysis of data sampled nonuniformly in time.[J]. Physica D.1992,58:273-[11]M. Small, K. Judd, Detecting nonlinearity in experimental data, International Journal of Bifurcation and Chaos, 1998, 8(6), 1231-1244.
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出版歷程
  • 收稿日期:  1999-05-09
  • 修回日期:  1999-11-15
  • 刊出日期:  2001-03-19

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