Heteroskedasticity testing through a comparison of Wald statistics

• Autor(a) principal: Murteira, José M.R.
• Data de Publicação: 2013
• Outros Autores: Ramalho, Esmeralda A., Ramalho, Joaquim J.S.
• 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
• topic: Heteroskedasticity testing; White test; Wald test; Supremum

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.