一种时间序列的弱非线性检验方法  

A test method for weak nonlinearity in time series

作　　者：姜可宇[1] 蔡志明[1] 陆振波[1] 

机构地区：[1]海军工程大学电子工程学院,武汉430033

出　　处：《物理学报》2008年第3期1471-1476,共6页Acta Physica Sinica

基　　金：国家重点基础研究发展规划项目(批准号:5132102ZZT32)资助的课题~~

摘　　要：时间序列的非线性是判定该时间序列具有混沌特性的必要条件.提出一种基于线性和非线性AR模型归一化多步预测误差比值的非线性检验量δNAR,采用替代数据法来检测时间序列中的弱非线性.以Lorenz时间序列为例,分析了估计非线性检验量δNAR时各相关参数对弱非线性检测性能的影响.通过混沌时间序列非线性检测试验,对4种混沌时间序列中的3种,非线性检验量δNAR都表现出比基于AIC模型选择准则的非线性检验量δAIC和非线性零阶预测误差δZP更强的弱非线性检测能力,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,具有最佳非线性检测效果的参数比较稳定,这为其他时间序列弱非线性检测的参数选择提供了参考.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.

关 键 词：替代数据 混沌时间序列 非线性AR模型 非线性检验 

分 类 号：O415.5[理学—理论物理]