METHODS article
Front. Netw. Physiol.
Sec. Information Theory
This article is part of the Research TopicEvaluated Methods for Signal Analysis: Promoting Open Science in Network PhysiologyView all 3 articles
Quantifying Coupling and Causality in Dynamic Bivariate Systems: a Unified Framework for Time-Domain, Spectral, and Information-Theoretic Analysis
Provisionally accepted
Laura Sparacino1
Hélder Pinto2
Chiara Barà1
Yuri Antonacci1
Riccardo Pernice1
Ana Paula Rocha2
Luca Faes1*- 1University of Palermo, Palermo, Italy
- 2Universidade do Porto, Porto, Portugal
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Understanding the underlying dynamics of complex real-world systems, such as neurophysiological and climate systems, requires quantifying the functional interactions between the system units under different scenarios. This tutorial paper offers a comprehensive description to time, frequency and information-theoretic domain measures for assessing the interdependence between pairs of time series describing the dynamical activities of physical systems, supporting flexible and robust analyses of statistical dependencies and directional relationships. Classical time and frequency domain correlation-based measures, as well as directional approaches derived from the notion of Granger causality, are introduced and discussed, along with information-theoretic measures of symmetrical and directional coupling. Both linear model-based and non-linear model-free estimation approaches are thoroughly described, the latter including binning, permutation, and nearest-neighbour estimators. Special emphasis is placed on the description of a unified framework that establishes a connection between causal and symmetric, as well as spectral and information-theoretic measures. This framework enables the frequency-specific representation of information-theoretic metrics, allowing for a detailed investigation of oscillatory components in bivariate systems. The practical computation of the interaction measures is favoured by presenting a software toolbox and two exemplary applications to cardiovascular and climate data. By bridging theoretical concepts with practical tools, this work enables researchers to effectively investigate a wide range of dynamical behaviours in various real-world scenarios in Network Physiology and beyond.
Keywords: Correlation, causality, information dynamics, spectral integration property, parametric autoregressive models, networkphysiology
Received: 16 Aug 2025; Accepted: 13 Nov 2025.
Copyright: © 2025 Sparacino, Pinto, Barà, Antonacci, Pernice, Rocha and Faes. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Luca Faes, luca.faes@unipa.it
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