Statistical properties of the entropy from ordinal patterns

Autores
Chagas, Eduarda; Frery, Alejandro César; Gambini, Juliana; Lucini, María Magdalena; Ramos, Heitor; Rey, Andrea Alejandra
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The ultimate purpose of the statistical analysis of ordinal patterns is to characterize the distribution of the features they induce. In particular, knowing the joint distribution of the pair entropy-statistical complexity for a large class of time series models would allow statistical tests that are unavailable to date. Working in this direction, we characterize the asymptotic distribution of the empirical Shannon's entropy for any model under which the true normalized entropy is neither zero nor one. We obtain the asymptotic distribution from the central limit theorem (assuming large time series), the multivariate delta method, and a third-order correction of its mean value. We discuss the applicability of other results (exact, first-, and second-order corrections) regarding their accuracy and numerical stability. Within a general framework for building test statistics about Shannon's entropy, we present a bilateral test that verifies if there is enough evidence to reject the hypothesis that two signals produce ordinal patterns with the same Shannon's entropy. We applied this bilateral test to the daily maximum temperature time series from three cities (Dublin, Edinburgh, and Miami) and obtained sensible results.
Fil: Chagas, Eduarda. Universidade Federal de Minas Gerais; Brasil
Fil: Frery, Alejandro César. Victoria University Of Wellington; Nueva Zelanda
Fil: Gambini, Juliana. Instituto Tecnológico de Buenos Aires; Argentina
Fil: Lucini, María Magdalena. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste; Argentina
Fil: Ramos, Heitor. Universidade Federal de Minas Gerais; Brasil
Fil: Rey, Andrea Alejandra. Universidad Tecnológica Nacional. Facultad Regional Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
ORDINAL PATTERNS
SHANNON ENTROPY
TIME SERIES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/217269
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Statistical properties of the entropy from ordinal patternsChagas, EduardaFrery, Alejandro CésarGambini, JulianaLucini, María MagdalenaRamos, HeitorRey, Andrea AlejandraORDINAL PATTERNSSHANNON ENTROPYTIME SERIEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The ultimate purpose of the statistical analysis of ordinal patterns is to characterize the distribution of the features they induce. In particular, knowing the joint distribution of the pair entropy-statistical complexity for a large class of time series models would allow statistical tests that are unavailable to date. Working in this direction, we characterize the asymptotic distribution of the empirical Shannon's entropy for any model under which the true normalized entropy is neither zero nor one. We obtain the asymptotic distribution from the central limit theorem (assuming large time series), the multivariate delta method, and a third-order correction of its mean value. We discuss the applicability of other results (exact, first-, and second-order corrections) regarding their accuracy and numerical stability. Within a general framework for building test statistics about Shannon's entropy, we present a bilateral test that verifies if there is enough evidence to reject the hypothesis that two signals produce ordinal patterns with the same Shannon's entropy. We applied this bilateral test to the daily maximum temperature time series from three cities (Dublin, Edinburgh, and Miami) and obtained sensible results.Fil: Chagas, Eduarda. Universidade Federal de Minas Gerais; BrasilFil: Frery, Alejandro César. Victoria University Of Wellington; Nueva ZelandaFil: Gambini, Juliana. Instituto Tecnológico de Buenos Aires; ArgentinaFil: Lucini, María Magdalena. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste; ArgentinaFil: Ramos, Heitor. Universidade Federal de Minas Gerais; BrasilFil: Rey, Andrea Alejandra. Universidad Tecnológica Nacional. Facultad Regional Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmerican Institute of Physics2022-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/217269Chagas, Eduarda; Frery, Alejandro César; Gambini, Juliana; Lucini, María Magdalena; Ramos, Heitor; et al.; Statistical properties of the entropy from ordinal patterns; American Institute of Physics; Chaos; 32; 11; 11-2022; 1-141054-1500CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1063/5.0118706info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:09:12Zoai:ri.conicet.gov.ar:11336/217269instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:09:13.135CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Statistical properties of the entropy from ordinal patterns
title Statistical properties of the entropy from ordinal patterns
spellingShingle Statistical properties of the entropy from ordinal patterns
Chagas, Eduarda
ORDINAL PATTERNS
SHANNON ENTROPY
TIME SERIES
title_short Statistical properties of the entropy from ordinal patterns
title_full Statistical properties of the entropy from ordinal patterns
title_fullStr Statistical properties of the entropy from ordinal patterns
title_full_unstemmed Statistical properties of the entropy from ordinal patterns
title_sort Statistical properties of the entropy from ordinal patterns
dc.creator.none.fl_str_mv Chagas, Eduarda
Frery, Alejandro César
Gambini, Juliana
Lucini, María Magdalena
Ramos, Heitor
Rey, Andrea Alejandra
author Chagas, Eduarda
author_facet Chagas, Eduarda
Frery, Alejandro César
Gambini, Juliana
Lucini, María Magdalena
Ramos, Heitor
Rey, Andrea Alejandra
author_role author
author2 Frery, Alejandro César
Gambini, Juliana
Lucini, María Magdalena
Ramos, Heitor
Rey, Andrea Alejandra
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv ORDINAL PATTERNS
SHANNON ENTROPY
TIME SERIES
topic ORDINAL PATTERNS
SHANNON ENTROPY
TIME SERIES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The ultimate purpose of the statistical analysis of ordinal patterns is to characterize the distribution of the features they induce. In particular, knowing the joint distribution of the pair entropy-statistical complexity for a large class of time series models would allow statistical tests that are unavailable to date. Working in this direction, we characterize the asymptotic distribution of the empirical Shannon's entropy for any model under which the true normalized entropy is neither zero nor one. We obtain the asymptotic distribution from the central limit theorem (assuming large time series), the multivariate delta method, and a third-order correction of its mean value. We discuss the applicability of other results (exact, first-, and second-order corrections) regarding their accuracy and numerical stability. Within a general framework for building test statistics about Shannon's entropy, we present a bilateral test that verifies if there is enough evidence to reject the hypothesis that two signals produce ordinal patterns with the same Shannon's entropy. We applied this bilateral test to the daily maximum temperature time series from three cities (Dublin, Edinburgh, and Miami) and obtained sensible results.
Fil: Chagas, Eduarda. Universidade Federal de Minas Gerais; Brasil
Fil: Frery, Alejandro César. Victoria University Of Wellington; Nueva Zelanda
Fil: Gambini, Juliana. Instituto Tecnológico de Buenos Aires; Argentina
Fil: Lucini, María Magdalena. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste; Argentina
Fil: Ramos, Heitor. Universidade Federal de Minas Gerais; Brasil
Fil: Rey, Andrea Alejandra. Universidad Tecnológica Nacional. Facultad Regional Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description The ultimate purpose of the statistical analysis of ordinal patterns is to characterize the distribution of the features they induce. In particular, knowing the joint distribution of the pair entropy-statistical complexity for a large class of time series models would allow statistical tests that are unavailable to date. Working in this direction, we characterize the asymptotic distribution of the empirical Shannon's entropy for any model under which the true normalized entropy is neither zero nor one. We obtain the asymptotic distribution from the central limit theorem (assuming large time series), the multivariate delta method, and a third-order correction of its mean value. We discuss the applicability of other results (exact, first-, and second-order corrections) regarding their accuracy and numerical stability. Within a general framework for building test statistics about Shannon's entropy, we present a bilateral test that verifies if there is enough evidence to reject the hypothesis that two signals produce ordinal patterns with the same Shannon's entropy. We applied this bilateral test to the daily maximum temperature time series from three cities (Dublin, Edinburgh, and Miami) and obtained sensible results.
publishDate 2022
dc.date.none.fl_str_mv 2022-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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://hdl.handle.net/11336/217269
Chagas, Eduarda; Frery, Alejandro César; Gambini, Juliana; Lucini, María Magdalena; Ramos, Heitor; et al.; Statistical properties of the entropy from ordinal patterns; American Institute of Physics; Chaos; 32; 11; 11-2022; 1-14
1054-1500
CONICET Digital
CONICET
url http://hdl.handle.net/11336/217269
identifier_str_mv Chagas, Eduarda; Frery, Alejandro César; Gambini, Juliana; Lucini, María Magdalena; Ramos, Heitor; et al.; Statistical properties of the entropy from ordinal patterns; American Institute of Physics; Chaos; 32; 11; 11-2022; 1-14
1054-1500
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1063/5.0118706
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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