Improved Surrogate Data for Nonlinearity Tests

TLDR

Current nonlinearity tests compare a time series to a Gaussian linear stochastic process null, using random surrogates constrained by the data’s linear properties. The authors propose a more general null hypothesis that permits nonlinear rescalings of a Gaussian linear process. They introduce an iterative algorithm that generates surrogates preserving both the autocorrelation structure and the probability distribution of the original data. The study demonstrates that such rescalings cannot be captured by simple amplitude adjustments, which otherwise cause spurious nonlinearity detections.

Abstract

Current tests for nonlinearity compare a time series to the null hypothesis of a Gaussian linear stochastic process. For this restricted null assumption, random surrogates can be constructed which are constrained by the linear properties of the data. We propose a more general null hypothesis allowing for nonlinear rescalings of a Gaussian linear process. We show that such rescalings cannot be accounted for by a simple amplitude adjustment of the surrogates which leads to spurious detection of nonlinearity. An iterative algorithm is proposed to make appropriate surrogates which have the same autocorrelations as the data and the same probability distribution.