Spectral Dependence

TL;DR

This paper introduces a comprehensive framework for analyzing dependence in multivariate time series by decomposing signals into frequency components, capturing both linear and non-linear dependencies, and applying it to EEG data.

Contribution

It provides a unifying approach that generalizes existing frequency domain measures and incorporates phase-amplitude coupling and causality analysis for multivariate signals.

Findings

Frequency domain measures like coherence are special cases of the framework.

The framework captures both instantaneous and lagged dependencies.

Applications to EEG data demonstrate its effectiveness.

Abstract

This paper presents a general framework for modeling dependence in multivariate time series. Its fundamental approach relies on decomposing each signal in a system into various frequency components and then studying the dependence properties through these oscillatory activities.The unifying theme across the paper is to explore the strength of dependence and possible lead-lag dynamics through filtering. The proposed framework is capable of representing both linear and non-linear dependencies that could occur instantaneously or after some delay(lagged dependence). Examples for studying dependence between oscillations are illustrated through multichannel electroencephalograms. These examples emphasized that some of the most prominent frequency domain measures such as coherence, partial coherence,and dual-frequency coherence can be derived as special cases under this general framework.This paper also introduces related approaches for modeling dependence through phase-amplitude coupling and causality of (one-sided) filtered signals.