Dissecting the multivariate extremal index and tail dependence
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/72724 |
Resumo: | A central issue in the theory of extreme values focuses on suitable conditions such that the well-known results for the limiting distributions of the maximum of i.i.d. sequences can be applied to stationary ones. In this context, the extremal index appears as a key parameter to capture the effect of temporal dependence on the limiting distribution of the maxima. The multivariate extremal index corresponds to a generalization of this concept to a multivariate context and affects the tail dependence structure within the marginal sequences and between them. As it is a function, the inference becomes more difficult, and it is therefore important to obtain characterizations, namely bounds based on the marginal dependence that are easier to estimate. In this work we present two decompositions that emphasize different types of information contained in the multivariate extremal index, an upper limit better than those found in the literature and we analyse its role in dependence on the limiting model of the componentwise maxima of a stationary sequence. We will illustrate the results with examples of recognized interest in applications. |
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Dissecting the multivariate extremal index and tail dependenceMultivariate extreme valuesMultivariate extremal indexTail dependenceExtremal coefficientsMadogramCiências Naturais::MatemáticasScience & TechnologyA central issue in the theory of extreme values focuses on suitable conditions such that the well-known results for the limiting distributions of the maximum of i.i.d. sequences can be applied to stationary ones. In this context, the extremal index appears as a key parameter to capture the effect of temporal dependence on the limiting distribution of the maxima. The multivariate extremal index corresponds to a generalization of this concept to a multivariate context and affects the tail dependence structure within the marginal sequences and between them. As it is a function, the inference becomes more difficult, and it is therefore important to obtain characterizations, namely bounds based on the marginal dependence that are easier to estimate. In this work we present two decompositions that emphasize different types of information contained in the multivariate extremal index, an upper limit better than those found in the literature and we analyse its role in dependence on the limiting model of the componentwise maxima of a stationary sequence. We will illustrate the results with examples of recognized interest in applications.Fundação para a Ciência e Tecnologia (FCT)Instituto Nacional de Estatística (INE)Universidade do MinhoFerreira, HelenaFerreira, Marta Susana2020-102020-10-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/72724eng1645-67262183-0371https://www.ine.pt/revstat/pdf/REVSTAT_v18-n4-7.pdfinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:40:40Zoai:repositorium.sdum.uminho.pt:1822/72724Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:37:31.364466Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Dissecting the multivariate extremal index and tail dependence |
title |
Dissecting the multivariate extremal index and tail dependence |
spellingShingle |
Dissecting the multivariate extremal index and tail dependence Ferreira, Helena Multivariate extreme values Multivariate extremal index Tail dependence Extremal coefficients Madogram Ciências Naturais::Matemáticas Science & Technology |
title_short |
Dissecting the multivariate extremal index and tail dependence |
title_full |
Dissecting the multivariate extremal index and tail dependence |
title_fullStr |
Dissecting the multivariate extremal index and tail dependence |
title_full_unstemmed |
Dissecting the multivariate extremal index and tail dependence |
title_sort |
Dissecting the multivariate extremal index and tail dependence |
author |
Ferreira, Helena |
author_facet |
Ferreira, Helena Ferreira, Marta Susana |
author_role |
author |
author2 |
Ferreira, Marta Susana |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Ferreira, Helena Ferreira, Marta Susana |
dc.subject.por.fl_str_mv |
Multivariate extreme values Multivariate extremal index Tail dependence Extremal coefficients Madogram Ciências Naturais::Matemáticas Science & Technology |
topic |
Multivariate extreme values Multivariate extremal index Tail dependence Extremal coefficients Madogram Ciências Naturais::Matemáticas Science & Technology |
description |
A central issue in the theory of extreme values focuses on suitable conditions such that the well-known results for the limiting distributions of the maximum of i.i.d. sequences can be applied to stationary ones. In this context, the extremal index appears as a key parameter to capture the effect of temporal dependence on the limiting distribution of the maxima. The multivariate extremal index corresponds to a generalization of this concept to a multivariate context and affects the tail dependence structure within the marginal sequences and between them. As it is a function, the inference becomes more difficult, and it is therefore important to obtain characterizations, namely bounds based on the marginal dependence that are easier to estimate. In this work we present two decompositions that emphasize different types of information contained in the multivariate extremal index, an upper limit better than those found in the literature and we analyse its role in dependence on the limiting model of the componentwise maxima of a stationary sequence. We will illustrate the results with examples of recognized interest in applications. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-10 2020-10-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1822/72724 |
url |
http://hdl.handle.net/1822/72724 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1645-6726 2183-0371 https://www.ine.pt/revstat/pdf/REVSTAT_v18-n4-7.pdf |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Instituto Nacional de Estatística (INE) |
publisher.none.fl_str_mv |
Instituto Nacional de Estatística (INE) |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
|
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1799132909374799872 |