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Entropy 2018, 20(9), 665; https://doi.org/10.3390/e20090665

Assessing Time Series Reversibility through Permutation Patterns

1
Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, 28040 Madrid, Spain
2
Department of Computer Science, Faculty of Science and Technology, Universidade Nova de Lisboa, 2829-516 Lisboa, Portugal
3
SCALab UMR CNRS 9193, University of Lille, 59800 Villeneuve d’Ascq, France
*
Author to whom correspondence should be addressed.
Received: 3 August 2018 / Revised: 29 August 2018 / Accepted: 31 August 2018 / Published: 3 September 2018
(This article belongs to the Section Statistical Mechanics)
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Abstract

Time irreversibility, i.e., the lack of invariance of the statistical properties of a system under time reversal, is a fundamental property of all systems operating out of equilibrium. Time reversal symmetry is associated with important statistical and physical properties and is related to the predictability of the system generating the time series. Over the past fifteen years, various methods to quantify time irreversibility in time series have been proposed, but these can be computationally expensive. Here, we propose a new method, based on permutation entropy, which is essentially parameter-free, temporally local, yields straightforward statistical tests, and has fast convergence properties. We apply this method to the study of financial time series, showing that stocks and indices present a rich irreversibility dynamics. We illustrate the comparative methodological advantages of our method with respect to a recently proposed method based on visibility graphs, and discuss the implications of our results for financial data analysis and interpretation. View Full-Text
Keywords: time irreversibility; permutation entropy; visibility graphs; efficient market hypothesis time irreversibility; permutation entropy; visibility graphs; efficient market hypothesis
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Zanin, M.; Rodríguez-González, A.; Menasalvas Ruiz, E.; Papo, D. Assessing Time Series Reversibility through Permutation Patterns. Entropy 2018, 20, 665.

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