Irreversibility of symbolic time series: A cautionary tale

Many empirical time series are genuinely symbolic: Examples range from link activation patterns in network science, to DNA coding or firing patterns in neuroscience, to cryptography or combinatorics on words. In some other contexts, the underlying time series is actually real valued, and symbolizati...

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Authors: Arola-Fernández, Lluís, Lacasa, Lucas
Format: article
Status:Published version
Publication Date:2023
Country:España
Institution:Consejo Superior de Investigaciones Científicas (CSIC)
Repository:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/351648
Online Access:http://hdl.handle.net/10261/351648
http://arxiv.org/abs/2303.11868v1
Access Level:Open access
Keyword:Statistics and Probability
Nonlinear Sciences
Chaotic Dynamics
Physics - Data Analysis
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spelling Irreversibility of symbolic time series: A cautionary taleArola-Fernández, LluísLacasa, LucasStatistics and ProbabilityNonlinear SciencesChaotic DynamicsNonlinear SciencesPhysics - Data AnalysisMany empirical time series are genuinely symbolic: Examples range from link activation patterns in network science, to DNA coding or firing patterns in neuroscience, to cryptography or combinatorics on words. In some other contexts, the underlying time series is actually real valued, and symbolization is applied subsequently, as in symbolic dynamics of chaotic systems. Among several time series quantifiers, time series irreversibility-the difference between forward and backward statistics in stationary time series-is of great relevance. However, the irreversible character of symbolized time series is not always equivalent to the one of the underlying real-valued signal, leading to some misconceptions and confusion on interpretability. Such confusion is even bigger for binary time series-a classical way to encode chaotic trajectories via symbolic dynamics. In this paper we aim to clarify some usual misconceptions and provide theoretical grounding for the practical analysis-and interpretation-of time irreversibility in symbolic time series. We outline sources of irreversibility in stationary symbolic sequences coming from frequency asymmetries of nonpalindromic pairs which we enumerate, and prove that binary time series cannot show any irreversibility based on words of length m<4, thus discussing the implications and sources of confusion. We also study irreversibility in the context of symbolic dynamics, and clarify why these can be reversible even when the underlying dynamical system is not, such as the case of the fully chaotic logistic map.We acknowledge funding from project DYNDEEP (Grant No. EUR2021-122007) from the Agencia Estatal de Investigación. L.L. additionally acknowledges funding from project MISLAND (Grant No. PID2020-114324GB-C22) and María de Maeztu Project No. CEX2021-001164-M, all funded by MCIN/AEI/10.13039/501100011033.With funding from the Spanish government through the "Severo Ochoa Centre of Excellence" accreditation (CEX2021-001164-M).Peer reviewedAmerican Physical SocietyAgencia Estatal de Investigación (España)Ministerio de Ciencia e Innovación (España)[Arola-Fernández, Lluís 0000-0001-6810-455X]Lacasa, Lucas [0000-0003-3057-0357]Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202420242023info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Publisher's versioninfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10261/351648http://arxiv.org/abs/2303.11868v1reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-114324GB-C22info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/CEX2021-001164-Mhttps://doi.org/10.1103/PhysRevE.108.014201Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/3516482026-05-22T06:33:51Z
dc.title.none.fl_str_mv Irreversibility of symbolic time series: A cautionary tale
title Irreversibility of symbolic time series: A cautionary tale
spellingShingle Irreversibility of symbolic time series: A cautionary tale
Arola-Fernández, Lluís
Statistics and Probability
Nonlinear Sciences
Chaotic Dynamics
Nonlinear Sciences
Physics - Data Analysis
title_short Irreversibility of symbolic time series: A cautionary tale
title_full Irreversibility of symbolic time series: A cautionary tale
title_fullStr Irreversibility of symbolic time series: A cautionary tale
title_full_unstemmed Irreversibility of symbolic time series: A cautionary tale
title_sort Irreversibility of symbolic time series: A cautionary tale
dc.creator.none.fl_str_mv Arola-Fernández, Lluís
Lacasa, Lucas
author Arola-Fernández, Lluís
author_facet Arola-Fernández, Lluís
Lacasa, Lucas
author_role author
author2 Lacasa, Lucas
author2_role author
dc.contributor.none.fl_str_mv Agencia Estatal de Investigación (España)
Ministerio de Ciencia e Innovación (España)
[Arola-Fernández, Lluís 0000-0001-6810-455X]
Lacasa, Lucas [0000-0003-3057-0357]
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Statistics and Probability
Nonlinear Sciences
Chaotic Dynamics
Nonlinear Sciences
Physics - Data Analysis
topic Statistics and Probability
Nonlinear Sciences
Chaotic Dynamics
Nonlinear Sciences
Physics - Data Analysis
description Many empirical time series are genuinely symbolic: Examples range from link activation patterns in network science, to DNA coding or firing patterns in neuroscience, to cryptography or combinatorics on words. In some other contexts, the underlying time series is actually real valued, and symbolization is applied subsequently, as in symbolic dynamics of chaotic systems. Among several time series quantifiers, time series irreversibility-the difference between forward and backward statistics in stationary time series-is of great relevance. However, the irreversible character of symbolized time series is not always equivalent to the one of the underlying real-valued signal, leading to some misconceptions and confusion on interpretability. Such confusion is even bigger for binary time series-a classical way to encode chaotic trajectories via symbolic dynamics. In this paper we aim to clarify some usual misconceptions and provide theoretical grounding for the practical analysis-and interpretation-of time irreversibility in symbolic time series. We outline sources of irreversibility in stationary symbolic sequences coming from frequency asymmetries of nonpalindromic pairs which we enumerate, and prove that binary time series cannot show any irreversibility based on words of length m<4, thus discussing the implications and sources of confusion. We also study irreversibility in the context of symbolic dynamics, and clarify why these can be reversible even when the underlying dynamical system is not, such as the case of the fully chaotic logistic map.
publishDate 2023
dc.date.none.fl_str_mv 2023
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Publisher's version
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/351648
http://arxiv.org/abs/2303.11868v1
url http://hdl.handle.net/10261/351648
http://arxiv.org/abs/2303.11868v1
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
#PLACEHOLDER_PARENT_METADATA_VALUE#
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-114324GB-C22
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/CEX2021-001164-M
https://doi.org/10.1103/PhysRevE.108.014201
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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