Unifying concepts in information-theoretic time-series analysis
Journal:
arXiv
Published Date:
May 19, 2025
Abstract
Information theory is a powerful framework for quantifying complexity,
uncertainty, and dynamical structure in time-series data, with widespread
applicability across disciplines such as physics, finance, and neuroscience.
However, the literature on these measures remains fragmented, with
domain-specific terminologies, inconsistent mathematical notation, and
disparate visualization conventions that hinder interdisciplinary integration.
This work addresses these challenges by unifying key information-theoretic
time-series measures through shared semantic definitions, standardized
mathematical notation, and cohesive visual representations. We compare these
measures in terms of their theoretical foundations, computational formulations,
and practical interpretability -- mapping them onto a common conceptual space
through an illustrative case study with functional magnetic resonance imaging
time series in the brain. This case study exemplifies the complementary
insights these measures offer in characterizing the dynamics of complex neural
systems, such as signal complexity and information flow. By providing a
structured synthesis, our work aims to enhance interdisciplinary dialogue and
methodological adoption, which is particularly critical for reproducibility and
interoperability in computational neuroscience. More broadly, our framework
serves as a resource for researchers seeking to navigate and apply
information-theoretic time-series measures to diverse complex systems.
