Nonparametric Inference for Periodic Sequences

dc.contributor.authorSun, Ying
dc.contributor.authorHart, Jeffrey D.
dc.contributor.authorGenton, Marc G.
dc.contributor.institutionTexas A and M University, College Station, United States
dc.date.accessioned2016-02-25T13:50:56Z
dc.date.available2016-02-25T13:50:56Z
dc.date.issued2012-02
dc.description.abstractThis article proposes a nonparametric method for estimating the period and values of a periodic sequence when the data are evenly spaced in time. The period is estimated by a "leave-out-one-cycle" version of cross-validation (CV) and complements the periodogram, a widely used tool for period estimation. The CV method is computationally simple and implicitly penalizes multiples of the smallest period, leading to a "virtually" consistent estimator of integer periods. This estimator is investigated both theoretically and by simulation.We also propose a nonparametric test of the null hypothesis that the data have constantmean against the alternative that the sequence of means is periodic. Finally, our methodology is demonstrated on three well-known time series: the sunspots and lynx trapping data, and the El Niño series of sea surface temperatures. © 2012 American Statistical Association and the American Society for Quality.
dc.description.sponsorshipProfessor Hart's research was supported in part by NSF grant DMS-0604801. Professor Genton's research was partially supported by NSF (National Science Foundation) grant DMS1007504, and award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia.
dc.identifier.citationSun Y, Hart JD, Genton MG (2012) Nonparametric Inference for Periodic Sequences. Technometrics 54: 83–96. Available: http://dx.doi.org/10.1080/00401706.2012.650499.
dc.identifier.doi10.1080/00401706.2012.650499
dc.identifier.issn0040-1706
dc.identifier.issn1537-2723
dc.identifier.journalTechnometrics
dc.identifier.urihttp://hdl.handle.net/10754/599001
dc.publisherInforma UK Limited
dc.subjectConsistency
dc.subjectCross-validation
dc.subjectModel selection
dc.subjectNonparametric estimation
dc.subjectPeriod
dc.titleNonparametric Inference for Periodic Sequences
dc.typeArticle
display.details.left<span><h5>Type</h5>Article<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0001-6703-4270&spc.sf=dc.date.issued&spc.sd=DESC">Sun, Ying</a> <a href="https://orcid.org/0000-0001-6703-4270" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Hart, Jeffrey D.,equals">Hart, Jeffrey D.</a><br><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0001-6467-2998&spc.sf=dc.date.issued&spc.sd=DESC">Genton, Marc G.</a> <a href="https://orcid.org/0000-0001-6467-2998" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><br><h5>Date</h5>2012-02</span>
display.details.right<span><h5>Abstract</h5>This article proposes a nonparametric method for estimating the period and values of a periodic sequence when the data are evenly spaced in time. The period is estimated by a "leave-out-one-cycle" version of cross-validation (CV) and complements the periodogram, a widely used tool for period estimation. The CV method is computationally simple and implicitly penalizes multiples of the smallest period, leading to a "virtually" consistent estimator of integer periods. This estimator is investigated both theoretically and by simulation.We also propose a nonparametric test of the null hypothesis that the data have constantmean against the alternative that the sequence of means is periodic. Finally, our methodology is demonstrated on three well-known time series: the sunspots and lynx trapping data, and the El Niño series of sea surface temperatures. © 2012 American Statistical Association and the American Society for Quality.<br><br><h5>Citation</h5>Sun Y, Hart JD, Genton MG (2012) Nonparametric Inference for Periodic Sequences. Technometrics 54: 83–96. Available: http://dx.doi.org/10.1080/00401706.2012.650499.<br><br><h5>Acknowledgements</h5>Professor Hart's research was supported in part by NSF grant DMS-0604801. Professor Genton's research was partially supported by NSF (National Science Foundation) grant DMS1007504, and award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia.<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=Informa UK Limited,equals">Informa UK Limited</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=Technometrics,equals">Technometrics</a><br><br><h5>DOI</h5><a href="https://doi.org/10.1080/00401706.2012.650499">10.1080/00401706.2012.650499</a></span>
orcid.authorSun, Ying::0000-0001-6703-4270
orcid.authorHart, Jeffrey D.
orcid.authorGenton, Marc G.::0000-0001-6467-2998
orcid.id0000-0001-6467-2998
orcid.id0000-0001-6703-4270
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