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Article: A note on a Marčenko-Pastur type theorem for time series

TitleA note on a Marčenko-Pastur type theorem for time series
Authors
Yao, J
KeywordsHigh-dimensional sample covariance matrices
High-dimensional time series
Marčenko-Pastur distributions
Issue Date2012
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/stapro
Citation
Statistics And Probability Letters, 2012, v. 82 n. 1, p. 22-28 How to Cite?
DOI: http://dx.doi.org/10.1016/j.spl.2011.08.011
AbstractIn this note we develop an extension of the Marčenko-Pastur theorem to time series model with temporal correlations. The limiting spectral distribution (LSD) of the sample covariance matrix is characterised by an explicit equation for its Stieltjes transform depending on the spectral density of the time series. A numerical algorithm is then given to compute the density functions of these LSD's. © 2011 Elsevier B.V.
Persistent Identifierhttp://hdl.handle.net/10722/143792
ISSN
0167-7152
2021 Impact Factor: 0.718
2020 SCImago Journal Rankings: 0.576
ISI Accession Number ID
WOS:000298204800004
Funding AgencyGrant Number
HKU
Funding Information:

The author is grateful to Jack Silverstein for several insightful discussions on the problem studied here, particularly for pointing out to me the numerical method of Section 3. We also thank a referee for important comments on the paper. The research of the author was supported partly by a HKU Start Fund grant.

References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorYao, Jen_HK
dc.date.accessioned2011-12-21T08:55:57Z-
dc.date.available2011-12-21T08:55:57Z-
dc.date.issued2012en_HK
dc.identifier.citationStatistics And Probability Letters, 2012, v. 82 n. 1, p. 22-28en_HK
dc.identifier.issn0167-7152en_HK
dc.identifier.urihttp://hdl.handle.net/10722/143792-
dc.description.abstractIn this note we develop an extension of the Marčenko-Pastur theorem to time series model with temporal correlations. The limiting spectral distribution (LSD) of the sample covariance matrix is characterised by an explicit equation for its Stieltjes transform depending on the spectral density of the time series. A numerical algorithm is then given to compute the density functions of these LSD's. © 2011 Elsevier B.V.en_HK
dc.languageengen_US
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/staproen_HK
dc.relation.ispartofStatistics and Probability Lettersen_HK
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Statistics & Probability Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Statistics & Probability Letters, 2012, v. 82 n. 1, p. 22-28. DOI: 10.1016/j.spl.2011.08.011-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.subjectHigh-dimensional sample covariance matricesen_HK
dc.subjectHigh-dimensional time seriesen_HK
dc.subjectMarčenko-Pastur distributionsen_HK
dc.titleA note on a Marčenko-Pastur type theorem for time seriesen_HK
dc.typeArticleen_HK
dc.identifier.emailYao, J: jeffyao@hku.hken_HK
dc.identifier.authorityYao, J=rp01473en_HK
dc.description.naturepostprint-
dc.identifier.doi10.1016/j.spl.2011.08.011en_HK
dc.identifier.scopuseid_2-s2.0-80053555652en_HK
dc.identifier.hkuros198155en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-80053555652&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume82en_HK
dc.identifier.issue1en_HK
dc.identifier.spage22en_HK
dc.identifier.epage28en_HK
dc.identifier.isiWOS:000298204800004-
dc.publisher.placeNetherlandsen_HK
dc.identifier.scopusauthoridYao, J=7403503451en_HK
dc.identifier.issnl0167-7152-

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