Vector-valued generalized Ornstein–Uhlenbeck processes: Properties and parameter estimation

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorVoutilainen, Marko
dc.contributor.authorViitasaari, Lauri
dc.contributor.authorIlmonen, Pauliina
dc.contributor.authorTorres, Soledad
dc.contributor.authorTudor, Ciprian
dc.contributor.departmentDepartment of Mathematics and Systems Analysis
dc.contributor.departmentDepartment of Information and Service Management
dc.contributor.departmentStatistics and Mathematical Data Science
dc.date.accessioned2023-02-28T15:35:46Z
dc.date.available2023-02-28T15:35:46Z
dc.date.issued2022-09
dc.descriptionhttps://doi.org/10.1111/sjos.12552
dc.description.abstractGeneralizations of the Ornstein-Uhlenbeck process defined through Langevin equations, such as fractional Ornstein-Uhlenbeck processes, have recently received a lot of attention. However, most of the literature focuses on the one-dimensional case with Gaussian noise. In particular, estimation of the unknown parameter is widely studied under Gaussian stationary increment noise. In this article, we consider estimation of the unknown model parameter in the multidimensional version of the Langevin equation, where the parameter is a matrix and the noise is a general, not necessarily Gaussian, vector-valued process with stationary increments. Based on algebraic Riccati equations, we construct an estimator for the parameter matrix. Moreover, we prove the consistency of the estimator and derive its limiting distribution under natural assumptions. In addition, to motivate our work, we prove that the Langevin equation characterizes essentially all multidimensional stationary processes.en
dc.description.versionPeer revieweden
dc.format.extent31
dc.format.extent992-1022
dc.format.mimetypeapplication/pdf
dc.identifier.citationVoutilainen , M , Viitasaari , L , Ilmonen , P , Torres , S & Tudor , C 2022 , ' Vector-valued generalized Ornstein–Uhlenbeck processes: Properties and parameter estimation ' , Scandinavian Journal of Statistics , vol. 49 , no. 3 , pp. 992-1022 . https://doi.org/10.1111/sjos.12552en
dc.identifier.doi10.1111/sjos.12552
dc.identifier.issn0303-6898
dc.identifier.issn1467-9469
dc.identifier.otherPURE UUID: 4c0b86ae-6671-4cdd-b470-e25bafa3946a
dc.identifier.otherPURE ITEMURL: https://research.aalto.fi/en/publications/4c0b86ae-6671-4cdd-b470-e25bafa3946a
dc.identifier.otherPURE LINK: http://www.scopus.com/inward/record.url?scp=85112616395&partnerID=8YFLogxK
dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/100801145/Scandinavian_J_Statistics_2021_Voutilainen_Vector_valued_generalized_Ornstein_Uhlenbeck_processes_Properties_and.pdf
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/119878
dc.identifier.urnURN:NBN:fi:aalto-202302282216
dc.language.isoenen
dc.publisherWILEY-BLACKWELL
dc.relation.ispartofseriesScandinavian Journal of Statisticsen
dc.relation.ispartofseriesVolume 49, issue 3en
dc.rightsopenAccessen
dc.subject.keywordalgebraic Riccati equations
dc.subject.keywordconsistency
dc.subject.keywordLangevin equation
dc.subject.keywordmultivariate Ornstein–Uhlenbeck process
dc.subject.keywordnonparametric estimation
dc.subject.keywordstationary processes
dc.titleVector-valued generalized Ornstein–Uhlenbeck processes: Properties and parameter estimationen
dc.typeA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessäfi
dc.type.versionpublishedVersion
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