A test method for weak nonlinearity in time series

作者：Jiang Ke Yu^*; Cai Zhi Ming; Lu Zhen Bo

来源：Acta Physica Sinica, 2008, 57(3): 1471-1476.

• surrogate data
• chaotic time series
• nonlinear AR model
• nonlinearity test

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 delta(NAR) has better discrimination power for weak nonlinearity than the test statistic delta(AIC) based on AIC rules and the zeroth order nonlinear prediction error delta(zp), 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.

• 出版日期2008-3