非线性时间序列的替代数据检验方法研究

STUDY OF THE SURROGATE DATA METHOD FOR NONLINEARITY OF TIME SERIES

目前,替代数据方法已逐渐成为时间序列的非线性成分检验中广为采用的一种方法。但对于具有同原始数据的均值和方差的线性相关高斯过程的零假设,通常产生相应替代数据的FT(FourierTransform)算法不能很好地重构原始数据的Fourier频谱。本文对替代数据方法进行了研究,提出了一种改进的FT算法,使得替代数据既具有原始数据的均值和方差,又具有原始数据的Fourier频谱。利用Gauss数据和logistic方程产生的混沌时间序列数据,证明本文提出的改进算法是可行的,所产生的替代数据是合适的。

Currently, the surrogate data method has become a widely used method in testing nonlinearity of time series. However, for the null hypothesis of linearly autocorrelated Gaussian noise with the mean and variance of the raw data, the exiting FT algorithms of generating surrogate data can not reproduce 'pure' frequencies very well. In this paper, the surrogate data method is studied and an improved FT algorithms is proposed. Using the proposed algorithm, the surrogate data sets have the same mean, variance and Fourier spectrum with the original data. This FT algorithm is compared to the previous and proved feasible by using Guass series and chaos time series of the logistic system.