ON THE RELIABILITY OF THE SURROGATE DATA TEST FOR NONLINEARITY IN THE ANALYSIS OF NOISY TIME SERIES

Abstract

In the analysis of real world data, the surrogate data test is often performed in order to investigate nonlinearity in the data. The null hypothesis of the test is that the original time series is generated from a linear stochastic process possibly undergoing a nonlinear static transform. We argue against reported rejection of the null hypothesis and claims of evidence of nonlinearity based on a single nonlinear statistic. In particular, two schemes for the generation of surrogate data are examined, the amplitude adjusted Fourier transform (AAFT) and the iterated AAFT (IAFFT) and many nonlinear discriminating statistics are used for testing, i.e. the fit with the Volterra series of polynomials and the fit with local average mappings, the mutual information, the correlation dimension, the false nearest neighbors, the largest Lyapunov exponent and simple nonlinear averages (the three point autocorrelation and the time reversal asymmetry). The results on simulated data and real data (EEG and exchange rates) suggest that the test depends on the method and its parameters, the algorithm generating the surrogate data and the observational data of the examined process.