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dc.contributor.authorLevy-Leduc, Celineen_US
dc.contributor.authorBoistard, Heleneen_US
dc.contributor.authorMoulines, Ericen_US
dc.contributor.authorTaqqu, Murad S.en_US
dc.contributor.authorReisen, Valderio A.en_US
dc.date.accessioned2020-01-22T18:55:38Z
dc.date.available2020-01-22T18:55:38Z
dc.date.issued2011-03-01
dc.identifierhttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000287146400003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=6e74115fe3da270499c3d65c9b17d654
dc.identifier.citationCeline Levy-Leduc, Helene Boistard, Eric Moulines, Murad S Taqqu, Valderio A Reisen. 2011. "Robust estimation of the scale and of the autocovariance function of Gaussian short- and long-range dependent processes." JOURNAL OF TIME SERIES ANALYSIS, Volume 32, Issue 2, pp. 135 - 156 (22). https://doi.org/10.1111/j.1467-9892.2010.00688.x
dc.identifier.issn0143-9782
dc.identifier.urihttps://hdl.handle.net/2144/39132
dc.description.abstractA desirable property of an autocovariance estimator is to be robust to the presence of additive outliers. It is well-known that the sample autocovariance, being based on moments, does not have this property. Hence, the use of an autocovariance estimator which is robust to additive outliers can be very useful for time-series modeling. In this paper, the asymptotic properties of the robust scale and autocovariance estimators proposed by Rousseeuw and Croux (1993) and Genton and Ma (2000) are established for Gaussian processes, with either short-range or long-range dependence. It is shown in the short-range dependence setting that this robust estimator is asymptotically normal at the rate √n, where n is the number of observations. An explicit expression of the asymptotic variance is also given and compared to the asymptotic variance of the classical autocovariance estimator. In the long-range dependence setting, the limiting distribution displays the same behavior than that of the classical autocovariance estimator, with a Gaussian limit and rate √n when the Hurst parameter H is less 3/4 and with a non-Gaussian limit (belonging to the second Wiener chaos) with rate depending on the Hurst parameter when H ∈ (3/4,1). Some Monte-Carlo experiments are presented to illustrate our claims and the Nile River data is analyzed as an application. The theoretical results and the empirical evidence strongly suggest using the robust estimators as an alternative to estimate the dependence structure of Gaussian processes.en_US
dc.format.extentp. 135 - 156en_US
dc.languageEnglish
dc.language.isoen_US
dc.publisherWILEY-BLACKWELL PUBLISHING, INCen_US
dc.relation.ispartofJOURNAL OF TIME SERIES ANALYSIS
dc.subjectScience & technologyen_US
dc.subjectPhysical sciencesen_US
dc.subjectMathematics, interdisciplinary applicationsen_US
dc.subjectStatistics & probabilityen_US
dc.subjectMathematicsen_US
dc.subjectAutocovariance functionen_US
dc.subjectLong memoryen_US
dc.subjectRobustnessen_US
dc.subjectInfluence functionen_US
dc.subjectScale estimatoren_US
dc.subjectHadamard differentiabilityen_US
dc.subjectFunctional delta methoden_US
dc.subjectEmpirical processen_US
dc.subjectLimit theoremsen_US
dc.subjectU-statisticsen_US
dc.subjectTime-seriesen_US
dc.subjectOutliersen_US
dc.subjectStatisticsen_US
dc.subjectEconometricsen_US
dc.titleRobust estimation of the scale and of the autocovariance function of Gaussian short- and long-range dependent processesen_US
dc.typeArticleen_US
dc.description.versionFirst author draften_US
dc.identifier.doi10.1111/j.1467-9892.2010.00688.x
pubs.elements-sourceweb-of-scienceen_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Mathematics & Statisticsen_US
pubs.publication-statusPublisheden_US
dc.identifier.orcid0000-0002-1145-9082 (Taqqu, Murad S)
dc.identifier.mycv54272


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