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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 .
The alternative data method has been widely used as a statistical method to test nonlinear and chaotic time series.As the null hypothesis of the original surrogate data method is a linear Gaussian process, the nonlinear non-Gaussian process, especially the non-minimum phase process may be misjudged as non-linear In order to solve this problem, a non-minimum phase sequence inversion method based on power spectral equivalence is proposed and deduced in detail. Combining with the non-minimum phase autoregressive moving average model identification method based on higher-order cumulants, A new algorithm is generated for the alternative data of linear non-Gaussian process.The simulation results show that the above method successfully overcomes the deficiencies of the original alternative data method.