Bayesian analysis of extreme events with threshold estimation
Autor(a) principal: | |
---|---|
Data de Publicação: | 2004 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional do FGV (FGV Repositório Digital) |
Texto Completo: | http://hdl.handle.net/10438/12961 |
Resumo: | The aim of this paper is to analyze extremal events using Generalized Pareto Distributions (GPD), considering explicitly the uncertainty about the threshold. Current practice empirically determines this quantity and proceeds by estimating the GPD parameters based on data beyond it, discarding all the information available be10w the threshold. We introduce a mixture model that combines a parametric form for the center and a GPD for the tail of the distributions and uses all observations for inference about the unknown parameters from both distributions, the threshold inc1uded. Prior distribution for the parameters are indirectly obtained through experts quantiles elicitation. Posterior inference is available through Markov Chain Monte Carlo (MCMC) methods. Simulations are carried out in order to analyze the performance of our proposed mode1 under a wide range of scenarios. Those scenarios approximate realistic situations found in the literature. We also apply the proposed model to a real dataset, Nasdaq 100, an index of the financiai market that presents many extreme events. Important issues such as predictive analysis and model selection are considered along with possible modeling extensions. |
id |
FGV_fe8dff052bf8b8bba212c9135fa3983c |
---|---|
oai_identifier_str |
oai:repositorio.fgv.br:10438/12961 |
network_acronym_str |
FGV |
network_name_str |
Repositório Institucional do FGV (FGV Repositório Digital) |
repository_id_str |
3974 |
spelling |
Lopes, Hedibert FreitasAssunção, Cibele Noronha BehrensGamerman, DaniEscolas::EPGEFGV2014-12-22T13:44:41Z2014-12-22T13:44:41Z2004-08-20http://hdl.handle.net/10438/12961The aim of this paper is to analyze extremal events using Generalized Pareto Distributions (GPD), considering explicitly the uncertainty about the threshold. Current practice empirically determines this quantity and proceeds by estimating the GPD parameters based on data beyond it, discarding all the information available be10w the threshold. We introduce a mixture model that combines a parametric form for the center and a GPD for the tail of the distributions and uses all observations for inference about the unknown parameters from both distributions, the threshold inc1uded. Prior distribution for the parameters are indirectly obtained through experts quantiles elicitation. Posterior inference is available through Markov Chain Monte Carlo (MCMC) methods. Simulations are carried out in order to analyze the performance of our proposed mode1 under a wide range of scenarios. Those scenarios approximate realistic situations found in the literature. We also apply the proposed model to a real dataset, Nasdaq 100, an index of the financiai market that presents many extreme events. Important issues such as predictive analysis and model selection are considered along with possible modeling extensions.engFundação Getulio Vargas. Escola de Pós-graduação em EconomiaSeminários de Almoço da EPGETodo cuidado foi dispensado para respeitar os direitos autorais deste trabalho. Entretanto, caso esta obra aqui depositada seja protegida por direitos autorais externos a esta instituição, contamos com a compreensão do autor e solicitamos que o mesmo faça contato através do Fale Conosco para que possamos tomar as providências cabíveisinfo:eu-repo/semantics/openAccessBayesianExtreme value theoryMCMCMixture modelThreshold estimationEconomiaEconometriaBayesian analysis of extreme events with threshold estimationinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlereponame:Repositório Institucional do FGV (FGV Repositório Digital)instname:Fundação Getulio Vargas (FGV)instacron:FGVORIGINAL000349483_l864b.pdf000349483_l864b.pdfapplication/pdf781923https://repositorio.fgv.br/bitstreams/12fe41b9-6731-4523-bb40-ddfbb422b14b/download498b011e49eb994b487d2725be5b4f1cMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-84707https://repositorio.fgv.br/bitstreams/fa4ae115-500d-4677-842d-5d8474eb61ef/downloaddfb340242cced38a6cca06c627998fa1MD52TEXT000349483_l864b.pdf.txt000349483_l864b.pdf.txtExtracted texttext/plain44849https://repositorio.fgv.br/bitstreams/8e0748af-ec4c-41cd-9979-fcbce14b734d/downloadc3b75289d82a933f8c721bfa1035e60dMD57THUMBNAIL000349483_l864b.pdf.jpg000349483_l864b.pdf.jpgGenerated Thumbnailimage/jpeg5036https://repositorio.fgv.br/bitstreams/46559df2-6c3c-43b8-be1a-9ab564dc8a44/download4156d1b6979adf8fec4b5d2d0908636aMD5810438/129612023-11-09 03:44:37.574open.accessoai:repositorio.fgv.br:10438/12961https://repositorio.fgv.brRepositório InstitucionalPRIhttp://bibliotecadigital.fgv.br/dspace-oai/requestopendoar:39742023-11-09T03:44:37Repositório Institucional do FGV (FGV Repositório Digital) - Fundação Getulio Vargas (FGV)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 |
dc.title.eng.fl_str_mv |
Bayesian analysis of extreme events with threshold estimation |
title |
Bayesian analysis of extreme events with threshold estimation |
spellingShingle |
Bayesian analysis of extreme events with threshold estimation Lopes, Hedibert Freitas Bayesian Extreme value theory MCMC Mixture model Threshold estimation Economia Econometria |
title_short |
Bayesian analysis of extreme events with threshold estimation |
title_full |
Bayesian analysis of extreme events with threshold estimation |
title_fullStr |
Bayesian analysis of extreme events with threshold estimation |
title_full_unstemmed |
Bayesian analysis of extreme events with threshold estimation |
title_sort |
Bayesian analysis of extreme events with threshold estimation |
author |
Lopes, Hedibert Freitas |
author_facet |
Lopes, Hedibert Freitas Assunção, Cibele Noronha Behrens Gamerman, Dani |
author_role |
author |
author2 |
Assunção, Cibele Noronha Behrens Gamerman, Dani |
author2_role |
author author |
dc.contributor.unidadefgv.por.fl_str_mv |
Escolas::EPGE |
dc.contributor.affiliation.none.fl_str_mv |
FGV |
dc.contributor.author.fl_str_mv |
Lopes, Hedibert Freitas Assunção, Cibele Noronha Behrens Gamerman, Dani |
dc.subject.por.fl_str_mv |
Bayesian Extreme value theory |
topic |
Bayesian Extreme value theory MCMC Mixture model Threshold estimation Economia Econometria |
dc.subject.eng.fl_str_mv |
MCMC Mixture model Threshold estimation |
dc.subject.area.por.fl_str_mv |
Economia |
dc.subject.bibliodata.por.fl_str_mv |
Econometria |
description |
The aim of this paper is to analyze extremal events using Generalized Pareto Distributions (GPD), considering explicitly the uncertainty about the threshold. Current practice empirically determines this quantity and proceeds by estimating the GPD parameters based on data beyond it, discarding all the information available be10w the threshold. We introduce a mixture model that combines a parametric form for the center and a GPD for the tail of the distributions and uses all observations for inference about the unknown parameters from both distributions, the threshold inc1uded. Prior distribution for the parameters are indirectly obtained through experts quantiles elicitation. Posterior inference is available through Markov Chain Monte Carlo (MCMC) methods. Simulations are carried out in order to analyze the performance of our proposed mode1 under a wide range of scenarios. Those scenarios approximate realistic situations found in the literature. We also apply the proposed model to a real dataset, Nasdaq 100, an index of the financiai market that presents many extreme events. Important issues such as predictive analysis and model selection are considered along with possible modeling extensions. |
publishDate |
2004 |
dc.date.issued.fl_str_mv |
2004-08-20 |
dc.date.accessioned.fl_str_mv |
2014-12-22T13:44:41Z |
dc.date.available.fl_str_mv |
2014-12-22T13:44:41Z |
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/10438/12961 |
url |
http://hdl.handle.net/10438/12961 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartofseries.por.fl_str_mv |
Seminários de Almoço da EPGE |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Fundação Getulio Vargas. Escola de Pós-graduação em Economia |
publisher.none.fl_str_mv |
Fundação Getulio Vargas. Escola de Pós-graduação em Economia |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional do FGV (FGV Repositório Digital) instname:Fundação Getulio Vargas (FGV) instacron:FGV |
instname_str |
Fundação Getulio Vargas (FGV) |
instacron_str |
FGV |
institution |
FGV |
reponame_str |
Repositório Institucional do FGV (FGV Repositório Digital) |
collection |
Repositório Institucional do FGV (FGV Repositório Digital) |
bitstream.url.fl_str_mv |
https://repositorio.fgv.br/bitstreams/12fe41b9-6731-4523-bb40-ddfbb422b14b/download https://repositorio.fgv.br/bitstreams/fa4ae115-500d-4677-842d-5d8474eb61ef/download https://repositorio.fgv.br/bitstreams/8e0748af-ec4c-41cd-9979-fcbce14b734d/download https://repositorio.fgv.br/bitstreams/46559df2-6c3c-43b8-be1a-9ab564dc8a44/download |
bitstream.checksum.fl_str_mv |
498b011e49eb994b487d2725be5b4f1c dfb340242cced38a6cca06c627998fa1 c3b75289d82a933f8c721bfa1035e60d 4156d1b6979adf8fec4b5d2d0908636a |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 |
repository.name.fl_str_mv |
Repositório Institucional do FGV (FGV Repositório Digital) - Fundação Getulio Vargas (FGV) |
repository.mail.fl_str_mv |
|
_version_ |
1810023871893471232 |