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Article: Spectral distribution of the sample covariance of high-dimensional time series with unit roots

TitleSpectral distribution of the sample covariance of high-dimensional time series with unit roots
Authors
Onatski, AWang, C
KeywordsEmpirical spectral distribution
sample covariance
non-stationary time series
Stieltjes transform
Feller-Pareto distribution
Issue Date2022
PublisherAcademia Sinica, Institute of Statistical Science. The Journal's web site is located at http://www.stat.sinica.edu.tw/statistica/
Citation
Statistica Sinica, 2022, v. 32, p. 43-63 How to Cite?
DOI: http://dx.doi.org/10.5705/ss.202019.0046
AbstractWe study the empirical spectral distributions of two sample-covariance-type matrices associated with high-dimensional time series with unit roots. The first matrix is S = XX' /T, where X is an n × T data with rows represented by n i.i.d. copies of T consecutive observations of a difference-stationary process. The second matrix is W = n ∫01 Wn (t)Wn (t)' dt, where Wn (t) is an n-dimensional vector with i.i.d. Brownian motion components. We show that, as n and T diverge to infinity proportionally, the two distributions weakly converge to nonrandom limits. The limit corresponding to S has a density ϕ(x) that decays as x−3/2 when x → ∞. The limit corresponding to W is a Feller-Pareto distribution.
Persistent Identifierhttp://hdl.handle.net/10722/284857
ISSN
1017-0405
2023 Impact Factor: 1.5
2023 SCImago Journal Rankings: 1.368
ISI Accession Number ID
WOS:000739764600003

 

DC FieldValueLanguage
dc.contributor.authorOnatski, A-
dc.contributor.authorWang, C-
dc.date.accessioned2020-08-07T09:03:32Z-
dc.date.available2020-08-07T09:03:32Z-
dc.date.issued2022-
dc.identifier.citationStatistica Sinica, 2022, v. 32, p. 43-63-
dc.identifier.issn1017-0405-
dc.identifier.urihttp://hdl.handle.net/10722/284857-
dc.description.abstractWe study the empirical spectral distributions of two sample-covariance-type matrices associated with high-dimensional time series with unit roots. The first matrix is S = XX' /T, where X is an n × T data with rows represented by n i.i.d. copies of T consecutive observations of a difference-stationary process. The second matrix is W = n ∫<font size=-1><sub>0</sub></font><font size=-1><sup>1</sup></font> W<font size=-1><sub>n</sub></font> (t)W<font size=-1><sub>n</sub></font> (t)' dt, where W<font size=-1><sub>n</sub></font> (t) is an n-dimensional vector with i.i.d. Brownian motion components. We show that, as n and T diverge to infinity proportionally, the two distributions weakly converge to nonrandom limits. The limit corresponding to S has a density ϕ(x) that decays as x<font size=-1><sup>−3/2</sup></font> when x → ∞. The limit corresponding to W is a Feller-Pareto distribution.-
dc.languageeng-
dc.publisherAcademia Sinica, Institute of Statistical Science. The Journal's web site is located at http://www.stat.sinica.edu.tw/statistica/-
dc.relation.ispartofStatistica Sinica-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.subjectEmpirical spectral distribution-
dc.subjectsample covariance-
dc.subjectnon-stationary time series-
dc.subjectStieltjes transform-
dc.subjectFeller-Pareto distribution-
dc.titleSpectral distribution of the sample covariance of high-dimensional time series with unit roots-
dc.typeArticle-
dc.identifier.emailWang, C: stacw@hku.hk-
dc.identifier.authorityWang, C=rp02404-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.5705/ss.202019.0046-
dc.identifier.hkuros312274-
dc.identifier.volume32-
dc.identifier.spage43-
dc.identifier.epage63-
dc.identifier.isiWOS:000739764600003-
dc.publisher.placeTaiwan, Republic of China-
dc.identifier.issnl1017-0405-

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