Characterization of time series via Rényi complexity–entropy curves

Autores
Jauregui, Max; Zunino, Luciano José; Lenzi, Ervin K.; Mendes, Renio S.; Ribeiro, Haroldo V.
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
One of the most useful tools for distinguishing between chaotic and stochastic time series is the so-called complexity–entropy causality plane. This diagram involves two complexity measures: the Shannon entropy and the statistical complexity. Recently, this idea has been generalized by considering the Tsallis monoparametric generalization of the Shannon entropy, yielding complexity–entropy curves. These curves have proven to enhance the discrimination among different time series related to stochastic and chaotic processes of numerical and experimental nature. Here we further explore these complexity–entropy curves in the context of the Renyi entropy, which is another monoparametric generalization of the Shannon entropy. By combining the Renyi entropy with the proper generalization of the statistical complexity, we associate a parametric curve (the Renyi complexity–entropy curve) with a given time series. We explore this approach in a series of numerical and experimental applications, demonstrating the usefulness of this new technique for time series analysis. We show that the Renyi complexity–entropy curves enable the differentiation among time series of chaotic, stochastic, and periodic nature. In particular, time series of stochastic nature are associated with curves displaying positive curvature in a neighborhood of their initial points, whereas curves related to chaotic phenomena have a negative curvature; finally, periodic time series are represented by vertical straight lines.
Centro de Investigaciones Ópticas
Materia
Ciencias Exactas
Física
Time series
R'enyi entropy
Complexity measures
Ordinal patterns probabilities
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/125460

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network_name_str SEDICI (UNLP)
spelling Characterization of time series via Rényi complexity–entropy curvesJauregui, MaxZunino, Luciano JoséLenzi, Ervin K.Mendes, Renio S.Ribeiro, Haroldo V.Ciencias ExactasFísicaTime seriesR'enyi entropyComplexity measuresOrdinal patterns probabilitiesOne of the most useful tools for distinguishing between chaotic and stochastic time series is the so-called complexity–entropy causality plane. This diagram involves two complexity measures: the Shannon entropy and the statistical complexity. Recently, this idea has been generalized by considering the Tsallis monoparametric generalization of the Shannon entropy, yielding complexity–entropy curves. These curves have proven to enhance the discrimination among different time series related to stochastic and chaotic processes of numerical and experimental nature. Here we further explore these complexity–entropy curves in the context of the Renyi entropy, which is another monoparametric generalization of the Shannon entropy. By combining the Renyi entropy with the proper generalization of the statistical complexity, we associate a parametric curve (the Renyi complexity–entropy curve) with a given time series. We explore this approach in a series of numerical and experimental applications, demonstrating the usefulness of this new technique for time series analysis. We show that the Renyi complexity–entropy curves enable the differentiation among time series of chaotic, stochastic, and periodic nature. In particular, time series of stochastic nature are associated with curves displaying positive curvature in a neighborhood of their initial points, whereas curves related to chaotic phenomena have a negative curvature; finally, periodic time series are represented by vertical straight lines.Centro de Investigaciones Ópticas2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf74-85http://sedici.unlp.edu.ar/handle/10915/125460enginfo:eu-repo/semantics/altIdentifier/issn/0378-4371info:eu-repo/semantics/altIdentifier/arxiv/1801.05738v1info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physa.2018.01.026info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:29:54Zoai:sedici.unlp.edu.ar:10915/125460Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:29:54.521SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Characterization of time series via Rényi complexity–entropy curves
title Characterization of time series via Rényi complexity–entropy curves
spellingShingle Characterization of time series via Rényi complexity–entropy curves
Jauregui, Max
Ciencias Exactas
Física
Time series
R'enyi entropy
Complexity measures
Ordinal patterns probabilities
title_short Characterization of time series via Rényi complexity–entropy curves
title_full Characterization of time series via Rényi complexity–entropy curves
title_fullStr Characterization of time series via Rényi complexity–entropy curves
title_full_unstemmed Characterization of time series via Rényi complexity–entropy curves
title_sort Characterization of time series via Rényi complexity–entropy curves
dc.creator.none.fl_str_mv Jauregui, Max
Zunino, Luciano José
Lenzi, Ervin K.
Mendes, Renio S.
Ribeiro, Haroldo V.
author Jauregui, Max
author_facet Jauregui, Max
Zunino, Luciano José
Lenzi, Ervin K.
Mendes, Renio S.
Ribeiro, Haroldo V.
author_role author
author2 Zunino, Luciano José
Lenzi, Ervin K.
Mendes, Renio S.
Ribeiro, Haroldo V.
author2_role author
author
author
author
dc.subject.none.fl_str_mv Ciencias Exactas
Física
Time series
R'enyi entropy
Complexity measures
Ordinal patterns probabilities
topic Ciencias Exactas
Física
Time series
R'enyi entropy
Complexity measures
Ordinal patterns probabilities
dc.description.none.fl_txt_mv One of the most useful tools for distinguishing between chaotic and stochastic time series is the so-called complexity–entropy causality plane. This diagram involves two complexity measures: the Shannon entropy and the statistical complexity. Recently, this idea has been generalized by considering the Tsallis monoparametric generalization of the Shannon entropy, yielding complexity–entropy curves. These curves have proven to enhance the discrimination among different time series related to stochastic and chaotic processes of numerical and experimental nature. Here we further explore these complexity–entropy curves in the context of the Renyi entropy, which is another monoparametric generalization of the Shannon entropy. By combining the Renyi entropy with the proper generalization of the statistical complexity, we associate a parametric curve (the Renyi complexity–entropy curve) with a given time series. We explore this approach in a series of numerical and experimental applications, demonstrating the usefulness of this new technique for time series analysis. We show that the Renyi complexity–entropy curves enable the differentiation among time series of chaotic, stochastic, and periodic nature. In particular, time series of stochastic nature are associated with curves displaying positive curvature in a neighborhood of their initial points, whereas curves related to chaotic phenomena have a negative curvature; finally, periodic time series are represented by vertical straight lines.
Centro de Investigaciones Ópticas
description One of the most useful tools for distinguishing between chaotic and stochastic time series is the so-called complexity–entropy causality plane. This diagram involves two complexity measures: the Shannon entropy and the statistical complexity. Recently, this idea has been generalized by considering the Tsallis monoparametric generalization of the Shannon entropy, yielding complexity–entropy curves. These curves have proven to enhance the discrimination among different time series related to stochastic and chaotic processes of numerical and experimental nature. Here we further explore these complexity–entropy curves in the context of the Renyi entropy, which is another monoparametric generalization of the Shannon entropy. By combining the Renyi entropy with the proper generalization of the statistical complexity, we associate a parametric curve (the Renyi complexity–entropy curve) with a given time series. We explore this approach in a series of numerical and experimental applications, demonstrating the usefulness of this new technique for time series analysis. We show that the Renyi complexity–entropy curves enable the differentiation among time series of chaotic, stochastic, and periodic nature. In particular, time series of stochastic nature are associated with curves displaying positive curvature in a neighborhood of their initial points, whereas curves related to chaotic phenomena have a negative curvature; finally, periodic time series are represented by vertical straight lines.
publishDate 2018
dc.date.none.fl_str_mv 2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/125460
url http://sedici.unlp.edu.ar/handle/10915/125460
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0378-4371
info:eu-repo/semantics/altIdentifier/arxiv/1801.05738v1
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physa.2018.01.026
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
dc.format.none.fl_str_mv application/pdf
74-85
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
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repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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