Heteroskedasticity testing through a comparison of Wald statistics
Autor(a) principal: | |
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Data de Publicação: | 2013 |
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/10400.5/15703 |
Resumo: | This paper shows that a test for heteroskedasticity within the context of classical linear regression can be based on the difference between Wald statistics in heteroskedasticity-robust and nonrobust forms. The test is asymptotically distributed under the null hypothesis of homoskedasticity as chi-squared with one degree of freedom. The power of the test is sensitive to the choice of parametric restriction used by the Wald statistics, so the supremum of a range of individual test statistics is proposed. Two versions of a supremum-based test are considered: the first version does not have a known asymptotic null distribution, so the bootstrap is employed to approximate its empirical distribution. The second version has a known asymptotic distribution and, in some cases, is asymptotically pivotal under the null. A simulation study illustrates the use and finite-sample performance of both versions of the test. In this study, the bootstrap is found to provide better size control than asymptotic critical values, namely with heavy-tailed, asymmetric distributions of the covariates. In addition, the use of well-known modifications of the heteroskedasticity consistent covariance matrix estimator of OLS coefficients is also found to benefit the tests’ overall behaviour. |
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Heteroskedasticity testing through a comparison of Wald statisticsHeteroskedasticity testingWhite testWald testSupremumThis paper shows that a test for heteroskedasticity within the context of classical linear regression can be based on the difference between Wald statistics in heteroskedasticity-robust and nonrobust forms. The test is asymptotically distributed under the null hypothesis of homoskedasticity as chi-squared with one degree of freedom. The power of the test is sensitive to the choice of parametric restriction used by the Wald statistics, so the supremum of a range of individual test statistics is proposed. Two versions of a supremum-based test are considered: the first version does not have a known asymptotic null distribution, so the bootstrap is employed to approximate its empirical distribution. The second version has a known asymptotic distribution and, in some cases, is asymptotically pivotal under the null. A simulation study illustrates the use and finite-sample performance of both versions of the test. In this study, the bootstrap is found to provide better size control than asymptotic critical values, namely with heavy-tailed, asymmetric distributions of the covariates. In addition, the use of well-known modifications of the heteroskedasticity consistent covariance matrix estimator of OLS coefficients is also found to benefit the tests’ overall behaviour.Springer VerlagRepositório da Universidade de LisboaMurteira, José M.R.Ramalho, Esmeralda A.Ramalho, Joaquim J.S.2018-06-25T09:39:01Z2013-082013-08-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/15703engMurteira, José M.R.; Esmeralda A. Ramalho and Joaquim J.S. Ramalho (2013). "Heteroskedasticity testing through a comparison of Wald statistics". Portuguese Economic Journal, Vol. 12, No. 2: pp. 131-1601617-982X (print)10.1007/s10258-013-0087-xmetadata only accessinfo: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:RCAAP2023-11-12T01:31:27Zoai:www.repository.utl.pt:10400.5/15703Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:01:18.677257Repositório 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 |
Heteroskedasticity testing through a comparison of Wald statistics |
title |
Heteroskedasticity testing through a comparison of Wald statistics |
spellingShingle |
Heteroskedasticity testing through a comparison of Wald statistics Murteira, José M.R. Heteroskedasticity testing White test Wald test Supremum |
title_short |
Heteroskedasticity testing through a comparison of Wald statistics |
title_full |
Heteroskedasticity testing through a comparison of Wald statistics |
title_fullStr |
Heteroskedasticity testing through a comparison of Wald statistics |
title_full_unstemmed |
Heteroskedasticity testing through a comparison of Wald statistics |
title_sort |
Heteroskedasticity testing through a comparison of Wald statistics |
author |
Murteira, José M.R. |
author_facet |
Murteira, José M.R. Ramalho, Esmeralda A. Ramalho, Joaquim J.S. |
author_role |
author |
author2 |
Ramalho, Esmeralda A. Ramalho, Joaquim J.S. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Repositório da Universidade de Lisboa |
dc.contributor.author.fl_str_mv |
Murteira, José M.R. Ramalho, Esmeralda A. Ramalho, Joaquim J.S. |
dc.subject.por.fl_str_mv |
Heteroskedasticity testing White test Wald test Supremum |
topic |
Heteroskedasticity testing White test Wald test Supremum |
description |
This paper shows that a test for heteroskedasticity within the context of classical linear regression can be based on the difference between Wald statistics in heteroskedasticity-robust and nonrobust forms. The test is asymptotically distributed under the null hypothesis of homoskedasticity as chi-squared with one degree of freedom. The power of the test is sensitive to the choice of parametric restriction used by the Wald statistics, so the supremum of a range of individual test statistics is proposed. Two versions of a supremum-based test are considered: the first version does not have a known asymptotic null distribution, so the bootstrap is employed to approximate its empirical distribution. The second version has a known asymptotic distribution and, in some cases, is asymptotically pivotal under the null. A simulation study illustrates the use and finite-sample performance of both versions of the test. In this study, the bootstrap is found to provide better size control than asymptotic critical values, namely with heavy-tailed, asymmetric distributions of the covariates. In addition, the use of well-known modifications of the heteroskedasticity consistent covariance matrix estimator of OLS coefficients is also found to benefit the tests’ overall behaviour. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013-08 2013-08-01T00:00:00Z 2018-06-25T09:39:01Z |
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/10400.5/15703 |
url |
http://hdl.handle.net/10400.5/15703 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Murteira, José M.R.; Esmeralda A. Ramalho and Joaquim J.S. Ramalho (2013). "Heteroskedasticity testing through a comparison of Wald statistics". Portuguese Economic Journal, Vol. 12, No. 2: pp. 131-160 1617-982X (print) 10.1007/s10258-013-0087-x |
dc.rights.driver.fl_str_mv |
metadata only access info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
metadata only access |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Springer Verlag |
publisher.none.fl_str_mv |
Springer Verlag |
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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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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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1799131101344563200 |