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A bootstrapped spectral test for adequacy in weak ARMA models
Zhu, Ke1; Li, Wai Keung2
AbstractThis paper proposes a Cramer-von Mises (CM) test statistic to check the adequacy of weak ARMA models. Without posing a martingale difference assumption on the error terms, the asymptotic null distribution of the CM test is obtained. Moreover, this CM test is consistent, and has nontrivial power against the local alternative of order n(-1/2). Due to the unknown dependence of error terms and the estimation effects, a new block-wise random weighting method is constructed to bootstrap the critical values of the test statistic. The new method is easy to implement and its validity is justified. The theory is illustrated by a small simulation study and an application to S&P 500 stock index. (C) 2015 Elsevier B.V. All rights reserved.
KeywordBlock-wise random weighting method Diagnostic checking Least squares estimation Spectral test Weak ARMA models Wild bootstrap
Funding ProjectResearch Grants Council of the Hong Kong SAR Government, GRF grant[HKU703711P] ; National Natural Science Foundation of China[11201459] ; Academy of Mathematics and Systems Science, CAS[2014-cjrwlzx-zk] ; Key Laboratory of RCSDS, CAS
WOS Research AreaBusiness & Economics ; Mathematics ; Mathematical Methods In Social Sciences
WOS SubjectEconomics ; Mathematics, Interdisciplinary Applications ; Social Sciences, Mathematical Methods
WOS IDWOS:000356194000008
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Document Type期刊论文
Corresponding AuthorLi, Wai Keung
Affiliation1.Chinese Acad Sci, Inst Appl Math, Beijing, Peoples R China
2.Univ Hong Kong, Dept Stat & Actuarial Sci, Hong Kong, Hong Kong, Peoples R China
Recommended Citation
GB/T 7714
Zhu, Ke,Li, Wai Keung. A bootstrapped spectral test for adequacy in weak ARMA models[J]. JOURNAL OF ECONOMETRICS,2015,187(1):113-130.
APA Zhu, Ke,&Li, Wai Keung.(2015).A bootstrapped spectral test for adequacy in weak ARMA models.JOURNAL OF ECONOMETRICS,187(1),113-130.
MLA Zhu, Ke,et al."A bootstrapped spectral test for adequacy in weak ARMA models".JOURNAL OF ECONOMETRICS 187.1(2015):113-130.
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