Revisiting algorithms for generating surrogate time series

TL;DR

This paper critically examines surrogate data generation algorithms, revealing their tendency to produce correlated surrogates that hinder nonlinear analysis, and emphasizes the need for separate testing of static and dynamic nonlinearities.

Contribution

It highlights the limitations of current surrogate generation algorithms and proposes the importance of testing for static and dynamic nonlinearities separately.

Findings

Common algorithms often produce surrogates with Fourier phase correlations.

Such surrogates can lead to non-detection of nonlinearities.

Separate testing for static and dynamic nonlinearities is necessary.

Abstract

The method of surrogates is one of the key concepts of nonlinear data analysis. Here, we demonstrate that commonly used algorithms for generating surrogates often fail to generate truly linear time series. Rather, they create surrogate realizations with Fourier phase correlations leading to non-detections of nonlinearities. We argue that reliable surrogates can only be generated, if one tests separately for static and dynamic nonlinearities.