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Article: LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises

TitleLADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises
Authors
KeywordsSign-based portmanteau test
ARMA(p, q) models
Asymptotic normality
G/ARCH noises
Heavy-tailed noises
LADE
Random weighting approach
Self-weighted LADE
Strong consistency
Issue Date2015
Citation
Journal of the American Statistical Association, 2015, v. 110, n. 510, p. 784-794 How to Cite?
Abstract© 2015 American Statistical Association.This article develops a systematic procedure of statistical inference for the auto-regressive moving average (ARMA) model with unspecified and heavy-tailed heteroscedastic noises. We first investigate the least absolute deviation estimator (LADE) and the self-weighted LADE for the model. Both estimators are shown to be strongly consistent and asymptotically normal when the noise has a finite variance and infinite variance, respectively. The rates of convergence of the LADE and the self-weighted LADE are n − 1/2, which is faster than those of least-square estimator (LSE) for the ARMA model when the tail index of generalized auto-regressive conditional heteroskedasticity (GARCH) noises is in (0, 4], and thus they are more efficient in this case. Since their asymptotic covariance matrices cannot be estimated directly from the sample, we develop the random weighting approach for statistical inference under this nonstandard case. We further propose a novel sign-based portmanteau test for model adequacy. Simulation study is carried out to assess the performance of our procedure and one real illustrating example is given. Supplementary materials for this article are available online.
Persistent Identifierhttp://hdl.handle.net/10722/230993
ISSN
2015 Impact Factor: 1.725
2015 SCImago Journal Rankings: 3.447

 

DC FieldValueLanguage
dc.contributor.authorZhu, Ke-
dc.contributor.authorLing, Shiqing-
dc.date.accessioned2016-09-01T06:07:20Z-
dc.date.available2016-09-01T06:07:20Z-
dc.date.issued2015-
dc.identifier.citationJournal of the American Statistical Association, 2015, v. 110, n. 510, p. 784-794-
dc.identifier.issn0162-1459-
dc.identifier.urihttp://hdl.handle.net/10722/230993-
dc.description.abstract© 2015 American Statistical Association.This article develops a systematic procedure of statistical inference for the auto-regressive moving average (ARMA) model with unspecified and heavy-tailed heteroscedastic noises. We first investigate the least absolute deviation estimator (LADE) and the self-weighted LADE for the model. Both estimators are shown to be strongly consistent and asymptotically normal when the noise has a finite variance and infinite variance, respectively. The rates of convergence of the LADE and the self-weighted LADE are n <sup>− 1/2</sup>, which is faster than those of least-square estimator (LSE) for the ARMA model when the tail index of generalized auto-regressive conditional heteroskedasticity (GARCH) noises is in (0, 4], and thus they are more efficient in this case. Since their asymptotic covariance matrices cannot be estimated directly from the sample, we develop the random weighting approach for statistical inference under this nonstandard case. We further propose a novel sign-based portmanteau test for model adequacy. Simulation study is carried out to assess the performance of our procedure and one real illustrating example is given. Supplementary materials for this article are available online.-
dc.languageeng-
dc.relation.ispartofJournal of the American Statistical Association-
dc.subjectSign-based portmanteau test-
dc.subjectARMA(p, q) models-
dc.subjectAsymptotic normality-
dc.subjectG/ARCH noises-
dc.subjectHeavy-tailed noises-
dc.subjectLADE-
dc.subjectRandom weighting approach-
dc.subjectSelf-weighted LADE-
dc.subjectStrong consistency-
dc.titleLADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises-
dc.typeArticle-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.doi10.1080/01621459.2014.977386-
dc.identifier.scopuseid_2-s2.0-84936751255-
dc.identifier.volume110-
dc.identifier.issue510-
dc.identifier.spage784-
dc.identifier.epage794-
dc.identifier.eissn1537-274X-

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