Decomposing spectral and phasic differences in non-linear features between datasets

TL;DR

This paper introduces a method to decompose differences in non-linear features between datasets into spectral, phasic, and interaction components, enhancing analysis of complex systems without assuming data structure.

Contribution

It presents a novel null-model-based decomposition technique for non-linear features, distinguishing spectral and phasic effects in time series data.

Findings

Decomposition accurately isolates spectral and phasic contributions.

Method is assumption-free and applicable to various time series analyses.

Enhances understanding of non-linear phenomena in complex systems.

Abstract

When employing non-linear methods to characterise complex systems, it is important to determine to what extent they are capturing genuine non-linear phenomena that could not be assessed by simpler spectral methods. Specifically, we are concerned with the problem of quantifying spectral and phasic effects on an observed difference in a non-linear feature between two systems (or two states of the same system). Here we derive, from a sequence of null models, a decomposition of the difference in an observable into spectral, phasic, and spectrum-phase interaction components. Our approach makes no assumptions about the structure of the data and adds nuance to a wide range of time series analyses.