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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/125460
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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 |
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Universidad Nacional de La Plata |
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SEDICI (UNLP) - Universidad Nacional de La Plata |
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