A new regression-based tail index estimator: an application to exchange rates
Autor(a) principal: | |
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Data de Publicação: | 2015 |
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/10400.5/23988 |
Resumo: | In this paper, a new regression-based approach for the estimation of the tail index of heavy-tailed distributions is introduced. Comparatively to many procedures currently available in the literature, our method does not involve order statistics and can be applied in more general contexts than just Pareto. The procedure is in line with approaches used in experimental data analysis with fixed explanatory variables, and has several important features which are worth highlighting. First, it provides a bias reduction when compared to available regression-based methods and a fortiori over standard least-squares based estimators of the tail index. Second, it is more resilient to the choice of the tail length used in the estimation of the index than the widely used Hill estimator. Third, when the effect of the slowly varying function at infinity of the Pareto distribution (the so called second order behaviour of the Taylor expansion) vanishes slowly our estimator continues to perform satisfactorily, whereas the Hill estimator rapidly deteriorates. Fourth, our estimator performs well under dependence of unknown form. For inference purposes, we also provide a way to compute the asymptotic variance of the proposed estimator under time dependence and conditional heteroscedasticity. An empirical application of the procedure to exchange rates is also provided. |
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A new regression-based tail index estimator: an application to exchange ratesSpecific DistributionsFinancial EconometricsIn this paper, a new regression-based approach for the estimation of the tail index of heavy-tailed distributions is introduced. Comparatively to many procedures currently available in the literature, our method does not involve order statistics and can be applied in more general contexts than just Pareto. The procedure is in line with approaches used in experimental data analysis with fixed explanatory variables, and has several important features which are worth highlighting. First, it provides a bias reduction when compared to available regression-based methods and a fortiori over standard least-squares based estimators of the tail index. Second, it is more resilient to the choice of the tail length used in the estimation of the index than the widely used Hill estimator. Third, when the effect of the slowly varying function at infinity of the Pareto distribution (the so called second order behaviour of the Taylor expansion) vanishes slowly our estimator continues to perform satisfactorily, whereas the Hill estimator rapidly deteriorates. Fourth, our estimator performs well under dependence of unknown form. For inference purposes, we also provide a way to compute the asymptotic variance of the proposed estimator under time dependence and conditional heteroscedasticity. An empirical application of the procedure to exchange rates is also provided.Banco de PortugalRepositório da Universidade de LisboaNicolau, JoãoRodrigues, Paulo M. M.2022-04-01T21:11:52Z2015-112015-11-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/23988engNicolau, João e Paulo M. M. Rodrigues. 2015. “A new regression-based tail index estimator: an application to exchange rates” .Banco de Portugal. Economic and Research Department. Working Papers nº 14 | 2015.2182-0422info: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:RCAAP2023-04-09T01:31:37Zoai:www.repository.utl.pt:10400.5/23988Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:08:07.888612Repositório 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 |
A new regression-based tail index estimator: an application to exchange rates |
title |
A new regression-based tail index estimator: an application to exchange rates |
spellingShingle |
A new regression-based tail index estimator: an application to exchange rates Nicolau, João Specific Distributions Financial Econometrics |
title_short |
A new regression-based tail index estimator: an application to exchange rates |
title_full |
A new regression-based tail index estimator: an application to exchange rates |
title_fullStr |
A new regression-based tail index estimator: an application to exchange rates |
title_full_unstemmed |
A new regression-based tail index estimator: an application to exchange rates |
title_sort |
A new regression-based tail index estimator: an application to exchange rates |
author |
Nicolau, João |
author_facet |
Nicolau, João Rodrigues, Paulo M. M. |
author_role |
author |
author2 |
Rodrigues, Paulo M. M. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Repositório da Universidade de Lisboa |
dc.contributor.author.fl_str_mv |
Nicolau, João Rodrigues, Paulo M. M. |
dc.subject.por.fl_str_mv |
Specific Distributions Financial Econometrics |
topic |
Specific Distributions Financial Econometrics |
description |
In this paper, a new regression-based approach for the estimation of the tail index of heavy-tailed distributions is introduced. Comparatively to many procedures currently available in the literature, our method does not involve order statistics and can be applied in more general contexts than just Pareto. The procedure is in line with approaches used in experimental data analysis with fixed explanatory variables, and has several important features which are worth highlighting. First, it provides a bias reduction when compared to available regression-based methods and a fortiori over standard least-squares based estimators of the tail index. Second, it is more resilient to the choice of the tail length used in the estimation of the index than the widely used Hill estimator. Third, when the effect of the slowly varying function at infinity of the Pareto distribution (the so called second order behaviour of the Taylor expansion) vanishes slowly our estimator continues to perform satisfactorily, whereas the Hill estimator rapidly deteriorates. Fourth, our estimator performs well under dependence of unknown form. For inference purposes, we also provide a way to compute the asymptotic variance of the proposed estimator under time dependence and conditional heteroscedasticity. An empirical application of the procedure to exchange rates is also provided. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015-11 2015-11-01T00:00:00Z 2022-04-01T21:11:52Z |
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/10400.5/23988 |
url |
http://hdl.handle.net/10400.5/23988 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Nicolau, João e Paulo M. M. Rodrigues. 2015. “A new regression-based tail index estimator: an application to exchange rates” .Banco de Portugal. Economic and Research Department. Working Papers nº 14 | 2015. 2182-0422 |
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 |
Banco de Portugal |
publisher.none.fl_str_mv |
Banco de Portugal |
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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1799131175206256640 |