Fourier phase index for extracting signatures of determinism and nonlinear features in time series

Detecting determinism and nonlinear properties from empirical time series is highly nontrivial. Traditionally, nonlinear time series analysis is based on an error-prone phase space reconstruction that is only applicable for stationary, largely noise-free data from a low-dimensional system and requires the nontrivial adjustment of various parameters. We present a data-driven index based on Fourier phases that detects determinism at a well-defined significance level, without using Fourier transform surrogate data. It extracts nonlinear features, is robust to noise, provides time-frequency resolution by a double running window approach, and potentially distinguishes regular and chaotic dynamics. We test this method on data derived from dynamical models as well as on real-world data, namely, intracranial recordings of an epileptic patient and a series of density related variations of sediments of a paleolake in Tlaxcala, Mexico.