线性非高斯序列的替代数据检验新方法

替代数据法作为检验时间序列非线性和混沌的统计方法获得了广泛的应用.由于原替代数据法的零假设为线性高斯过程,可能把线性非高斯过程,特别是非最小相位过程误判为非线性.为了解决这一问题,提出并详细推导了基于功率谱等价的非最小相位序列求逆方法;结合基于高阶累积量的非最小相位自回归滑动平均模型辨识方法,提出了检验序列是否为线性非高斯过程的替代数据生成新算法.仿真算例表明,上述方法成功地克服了原替代数据法的不足. 关键词： 替代数据 非线性检验 非最小相位 功率谱等价

A NEW METHOD OF SURROGATE DATA TEST FOR LINEAR NON-GAUSSIAN TIME SERIES

Surrogate data testing is a popular method to detect nonlinearity and chaos in time series and has been widely used in many applications with erratic time series.With the explicit null hypothesis that the time series is generated from a linear,stochastic,Gaussian stationary process,the surrogate data test based on phase randomization may give false alarm for nonlinearity at a linear non-minimum phase non-Gaussian sequence.So,we propose a new method to test the hypothesis of linear non-Gaussian process in light of typical realization of surrogates.With the ARMA parameters estimated from high-order cumulants and the series itself,a method to estimate the input noise of a non-minimum phase sequence is developed based on power spectrum equivalence,which is the bottle-neck to generate surrogates for non-minimum phase time series.The results of numerical experiments confirm our approach to test non-minimum phase non-Gaussian process.