基于非线性AR模型的时间序列弱非线性检验方法

Nonlinear AR Model Based Test Method for Weak Nonlinearity in Time Series

提出一种基于非线性AR模型相对预测误差的非线性检验量δNAR,采用替代数据法来检验时间序列中的弱非线性.以4种混沌时间序列为例,分析并比较了非线性检验量δNAR与非线性零阶预测误差δZP的弱非线性检验能力.结果表明,对4种混沌时间序列中的3种,非线性检验量δNAR都表现出比非线性零阶预测误差δZP更强的弱非线性检验能力,表明该非线性检验量具有较强的数据适应性,而且对于不同的数据,具有最佳非线性检验效果的参数比较固定.

A new test statistic for nonlinearity,which is based on the nonlinear AR model, is used to detect the weak nonlinear components contained in time series using the surrogate data method.Taking example for 4 chaotic time series,the power of weak nonlinearity detection performance of the test statistic δNAR is analyzed and compared with the zeroth order nonlinear prediction error δZP.The results show that the proposed test statistic δNAR has better discrimination power for weak nonlinearity than δZP for 3 in 4 chaotic time series,and has strong adaptive abilities for time series.And,for different time series,the parameters with best nonlinearity discrimination performance are kept constant.