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Article: On testing for high-dimensional white noise

TitleOn testing for high-dimensional white noise
Authors
KeywordsLarge autocovariance matrix
Hosking test
Li–McLeod test
high-dimensional time series
random matrix theory
Issue Date2019
PublisherInstitute of Mathematical Statistics. The Journal's web site is located at http://www.imstat.org/aos/
Citation
The Annals of Statistics, 2019, v. 47 n. 6, p. 3382-3412 How to Cite?
AbstractTesting for white noise is a classical yet important problem in statistics, especially for diagnostic checks in time series modeling and linear regression. For high-dimensional time series in the sense that the dimension p is large in relation to the sample size T, the popular omnibus tests including the multivariate Hosking and Li–McLeod tests are extremely conservative, leading to substantial power loss. To develop more relevant tests for high-dimensional cases, we propose a portmanteau-type test statistic which is the sum of squared singular values of the first q lagged sample autocovariance matrices. It, therefore, encapsulates all the serial correlations (up to the time lag q) within and across all component series. Using the tools from random matrix theory and assuming both p and T diverge to infinity, we derive the asymptotic normality of the test statistic under both the null and a specific VMA(1) alternative hypothesis. As the actual implementation of the test requires the knowledge of three characteristic constants of the population cross-sectional covariance matrix and the value of the fourth moment of the standardized innovations, nontrivial estimations are proposed for these parameters and their integration leads to a practically usable test. Extensive simulation confirms the excellent finite-sample performance of the new test with accurate size and satisfactory power for a large range of finite (p,T) combinations, therefore, ensuring wide applicability in practice. In particular, the new tests are consistently superior to the traditional Hosking and Li–McLeod tests.
Persistent Identifierhttp://hdl.handle.net/10722/274046
ISSN
2023 Impact Factor: 3.2
2023 SCImago Journal Rankings: 5.335
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorLi, Z-
dc.contributor.authorLam, C-
dc.contributor.authorYao, J-
dc.contributor.authorYao, Q-
dc.date.accessioned2019-08-18T14:53:58Z-
dc.date.available2019-08-18T14:53:58Z-
dc.date.issued2019-
dc.identifier.citationThe Annals of Statistics, 2019, v. 47 n. 6, p. 3382-3412-
dc.identifier.issn0090-5364-
dc.identifier.urihttp://hdl.handle.net/10722/274046-
dc.description.abstractTesting for white noise is a classical yet important problem in statistics, especially for diagnostic checks in time series modeling and linear regression. For high-dimensional time series in the sense that the dimension p is large in relation to the sample size T, the popular omnibus tests including the multivariate Hosking and Li–McLeod tests are extremely conservative, leading to substantial power loss. To develop more relevant tests for high-dimensional cases, we propose a portmanteau-type test statistic which is the sum of squared singular values of the first q lagged sample autocovariance matrices. It, therefore, encapsulates all the serial correlations (up to the time lag q) within and across all component series. Using the tools from random matrix theory and assuming both p and T diverge to infinity, we derive the asymptotic normality of the test statistic under both the null and a specific VMA(1) alternative hypothesis. As the actual implementation of the test requires the knowledge of three characteristic constants of the population cross-sectional covariance matrix and the value of the fourth moment of the standardized innovations, nontrivial estimations are proposed for these parameters and their integration leads to a practically usable test. Extensive simulation confirms the excellent finite-sample performance of the new test with accurate size and satisfactory power for a large range of finite (p,T) combinations, therefore, ensuring wide applicability in practice. In particular, the new tests are consistently superior to the traditional Hosking and Li–McLeod tests.-
dc.languageeng-
dc.publisherInstitute of Mathematical Statistics. The Journal's web site is located at http://www.imstat.org/aos/-
dc.relation.ispartofThe Annals of Statistics-
dc.subjectLarge autocovariance matrix-
dc.subjectHosking test-
dc.subjectLi–McLeod test-
dc.subjecthigh-dimensional time series-
dc.subjectrandom matrix theory-
dc.titleOn testing for high-dimensional white noise-
dc.typeArticle-
dc.identifier.emailYao, J: jeffyao@hku.hk-
dc.identifier.authorityYao, J=rp01473-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1214/18-AOS1782-
dc.identifier.scopuseid_2-s2.0-85079174019-
dc.identifier.hkuros302067-
dc.identifier.volume47-
dc.identifier.issue6-
dc.identifier.spage3382-
dc.identifier.epage3412-
dc.identifier.isiWOS:000493896800014-
dc.publisher.placeUnited States-
dc.identifier.issnl0090-5364-

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