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A test method for weak nonlinearity in time series

Jiang Ke-Yu Cai Zhi-Ming Lu Zhen-Bo

A test method for weak nonlinearity in time series

Jiang Ke-Yu, Cai Zhi-Ming, Lu Zhen-Bo
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  • Abstract views:  3793
  • PDF Downloads:  1277
  • Cited By: 0
Publishing process
  • Received Date:  16 April 2007
  • Accepted Date:  18 June 2007
  • Published Online:  20 March 2008

A test method for weak nonlinearity in time series

  • 1. 海军工程大学电子工程学院,武汉 430033

Abstract: Nonlinearity is necessary for time series to be treated as chaotic time series. A new test statistic for nonlinearity, which is based on the ratio of the multistep normalized prediction error with respect to linear AR models and nonlinear AR models, is used to detect the weak nonlinear components contained in time series by the surrogate data method. Taking example for Lorenz time series, the effect of related parameters for test statistic estimation is analyzed. By the nonlinearity tests for chaotic time series, the proposed test statistic δNAR has better discrimination power for weak nonlinearity than the test statistic δAIC based on AIC rules and the zeroth order nonlinear prediction error δZP, which shows that the proposed test statistic has strong adaptive abilities for time series. And, for different time series, the parameters with best nonlinearity discrimination performance are kept constant. The stabilization of parameters facilitates the nonlinearity test for other time series.

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