Band-phase-randomized Surrogates to assess nonlinearity in non-stationary time series

TL;DR

This paper introduces a novel surrogate data method based on band-phase randomization to accurately detect nonlinearity in non-stationary time series, especially physiological signals like heart rate variability.

Contribution

The authors propose a new band-phase-randomized surrogate method that extends existing techniques to handle non-stationary data, improving nonlinearity detection accuracy.

Findings

Method effectively distinguishes linear stationarity, linear non-stationarity, and nonlinearity.

Successfully applied to heart rate variability data with nonstationarities.

Preserves linear correlations in surrogate data, unlike previous methods.

Abstract

Testing for nonlinearity is one of the most important preprocessing steps in nonlinear time series analysis. Typically, this is done by means of the linear surrogate data methods. But it is a known fact that the validity of the results heavily depends on the stationarity of the time series. Since most physiological signals are non-stationary, it is easy to falsely detect nonlinearity using the linear surrogate data methods. In this document, we propose a methodology to extend the procedure for generating constrained surrogate time series in order to assess nonlinearity in non-stationary data. The method is based on the band-phase-randomized surrogates, which consists (contrary to the linear surrogate data methods) in randomizing only a portion of the Fourier phases in the high frequency band. Analysis of simulated time series showed that in comparison to the linear surrogate data method, our method is able to discriminate between linear stationarity, linear non-stationary and nonlinear time series. When applying our methodology to heart rate variability (HRV) time series that present spikes and other kinds of nonstationarities, we where able to obtain surrogate time series that look like the data and preserves linear correlations, something that is not possible to do with the existing surrogate data methods.