Detecting Nonlinearity in Data with Long Coherence Times

TL;DR

This paper examines the limitations of common nonlinearity detection methods in long-coherence-time data, revealing they often falsely indicate nonlinearity in linear time series.

Contribution

It provides an analytical and experimental analysis of why existing techniques fail with long coherence times, highlighting their potential for false positives.

Findings

Both techniques tend to falsely detect nonlinearity in linear data with long coherence times.

Analytical and numerical evidence shows these methods are unreliable under certain conditions.

Long coherence time can cause misinterpretation of linear data as nonlinear.

Abstract

We consider the limitations of two techniques for detecting nonlinearity in time series. The first technique compares the original time series to an ensemble of surrogate time series that are constructed to mimic the linear properties of the original. The second technique compares the forecasting error of linear and nonlinear predictors. Both techniques are found to be problematic when the data has a long coherence time; they tend to indicate nonlinearity even for linear time series. We investigate the causes of these difficulties both analytically and with numerical experiments on ``real'' and computer-generated data. In particular, although we do see some initial evidence for nonlinear structure in the SFI dataset E, we are inclined to dismiss this evidence as an artifact of the long coherence time.