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Article: A robust goodness-of-fit test for generalized autoregressive conditional heteroscedastic models

TitleA robust goodness-of-fit test for generalized autoregressive conditional heteroscedastic models
Authors
KeywordsConditional heteroscedastic model
Goodness-of-fit test
Heavy tail
Residual empirical process
Robustness
Issue Date2018
PublisherOxford University Press. The Journal's web site is located at http://biomet.oxfordjournals.org/
Citation
Biometrika, 2018, v. 105 n. 1, p. 73-89 How to Cite?
AbstractThe estimation of time series models with heavy-tailed innovations has been widely discussed, but corresponding goodness-of-fit tests have attracted less attention, primarily because the autocorrelation function commonly used in constructing goodness-of-fit tests necessarily imposes certain moment conditions on the innovations. As a bounded random variable has finite moments of all orders, we address the problem by first transforming the residuals with a bounded function. More specifically, we consider the sample autocorrelation function of the transformed absolute residuals of a fitted generalized autoregressive conditional heteroscedastic model. With the corresponding residual empirical distribution function naturally employed as the transformation, a robust goodness-of-fit test is then constructed. The asymptotic distributions of the test statistic under the null hypothesis and local alternatives are derived, and Monte Carlo experiments are conducted to examine finite-sample properties. The proposed test is shown to be more powerful than existing tests when the innovations are heavy-tailed.
Persistent Identifierhttp://hdl.handle.net/10722/253572
ISSN
2019 Impact Factor: 1.632
2015 SCImago Journal Rankings: 2.801
SSRN
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorZheng, Y-
dc.contributor.authorLi, WK-
dc.contributor.authorLi, G-
dc.date.accessioned2018-05-21T02:59:48Z-
dc.date.available2018-05-21T02:59:48Z-
dc.date.issued2018-
dc.identifier.citationBiometrika, 2018, v. 105 n. 1, p. 73-89-
dc.identifier.issn0006-3444-
dc.identifier.urihttp://hdl.handle.net/10722/253572-
dc.description.abstractThe estimation of time series models with heavy-tailed innovations has been widely discussed, but corresponding goodness-of-fit tests have attracted less attention, primarily because the autocorrelation function commonly used in constructing goodness-of-fit tests necessarily imposes certain moment conditions on the innovations. As a bounded random variable has finite moments of all orders, we address the problem by first transforming the residuals with a bounded function. More specifically, we consider the sample autocorrelation function of the transformed absolute residuals of a fitted generalized autoregressive conditional heteroscedastic model. With the corresponding residual empirical distribution function naturally employed as the transformation, a robust goodness-of-fit test is then constructed. The asymptotic distributions of the test statistic under the null hypothesis and local alternatives are derived, and Monte Carlo experiments are conducted to examine finite-sample properties. The proposed test is shown to be more powerful than existing tests when the innovations are heavy-tailed.-
dc.languageeng-
dc.publisherOxford University Press. The Journal's web site is located at http://biomet.oxfordjournals.org/-
dc.relation.ispartofBiometrika-
dc.rightsThis is a pre-copyedited, author-produced version of an article accepted for publication in Biometrika following peer review. The version of record Biometrika, 2018, v. 105 n. 1, p. 73-89 is available online at: https://academic.oup.com/biomet/article-abstract/105/1/73/4653523?redirectedFrom=fulltext [DOI: https://doi.org/10.1093/biomet/asx063].-
dc.subjectConditional heteroscedastic model-
dc.subjectGoodness-of-fit test-
dc.subjectHeavy tail-
dc.subjectResidual empirical process-
dc.subjectRobustness-
dc.titleA robust goodness-of-fit test for generalized autoregressive conditional heteroscedastic models-
dc.typeArticle-
dc.identifier.emailLi, WK: hrntlwk@hkucc.hku.hk-
dc.identifier.emailLi, G: gdli@hku.hk-
dc.identifier.authorityLi, WK=rp00741-
dc.identifier.authorityLi, G=rp00738-
dc.description.naturepostprint-
dc.identifier.doi10.1093/biomet/asx063-
dc.identifier.scopuseid_2-s2.0-85043299739-
dc.identifier.hkuros285026-
dc.identifier.volume105-
dc.identifier.issue1-
dc.identifier.spage73-
dc.identifier.epage89-
dc.identifier.isiWOS:000426812700006-
dc.publisher.placeUnited Kingdom-
dc.identifier.ssrn2690099-
dc.identifier.issnl0006-3444-

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