Fractional iterated Ornstein-Uhlenbeck Processes

Kalemkerian, Juan - León, José Rafael

Resumen:

We present a Gaussian process that arises from the iteration of p fractional Ornstein–Uhlenbeck processes generated by the same fractional Brownian motion. When the values of the parameters defining the iteration are pairwise distinct, this iteration results in a particular linear combination of those processes. Although for H > 1=2 each term of the iteration is a long memory process, we prove that when p 2 the process obtained has short memory. We prove that the local Hölder index of the process is H, and obtain an explicit formula for the spectral density. We present a way to estimate the parameters and prove that the estimators are consistent and the results are asymptotically Gaussian. These processes can be used to model time series of long or short memory.


Detalles Bibliográficos
2019
Fractional Brownian motion
Fractional Ornstein-Uhlenbeck process
Long memory processes.
Inglés
Universidad de la República
COLIBRI
https://hdl.handle.net/20.500.12008/28486
Acceso abierto
Licencia Creative Commons Atribución (CC - By 4.0)
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author Kalemkerian, Juan
author2 León, José Rafael
author2_role author
author_facet Kalemkerian, Juan
León, José Rafael
author_role author
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collection COLIBRI
dc.contributor.filiacion.none.fl_str_mv Kalemkerian Juan, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.
León José Rafael, Universidad de la República (Uruguay). Facultad de Ingeniería
dc.creator.none.fl_str_mv Kalemkerian, Juan
León, José Rafael
dc.date.accessioned.none.fl_str_mv 2021-07-07T14:40:29Z
dc.date.available.none.fl_str_mv 2021-07-07T14:40:29Z
dc.date.issued.none.fl_str_mv 2019
dc.description.abstract.none.fl_txt_mv We present a Gaussian process that arises from the iteration of p fractional Ornstein–Uhlenbeck processes generated by the same fractional Brownian motion. When the values of the parameters defining the iteration are pairwise distinct, this iteration results in a particular linear combination of those processes. Although for H > 1=2 each term of the iteration is a long memory process, we prove that when p 2 the process obtained has short memory. We prove that the local Hölder index of the process is H, and obtain an explicit formula for the spectral density. We present a way to estimate the parameters and prove that the estimators are consistent and the results are asymptotically Gaussian. These processes can be used to model time series of long or short memory.
dc.format.extent.es.fl_str_mv 24 h.
dc.format.mimetype.es.fl_str_mv application/pdf
dc.identifier.citation.es.fl_str_mv Kalemkerian, J y León, J. "Fractional iterated Ornstein-Uhlenbeck Processes". Latin American Journal of Probability and Mathematical Statistics. [en línea] 2019, 16: 1105-1128. 24 h. DOI: 10.30757/ALEA.v.16-41
dc.identifier.doi.none.fl_str_mv 10.30757/ALEA.v16-41
dc.identifier.issn.none.fl_str_mv 1980-0436
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12008/28486
dc.language.iso.none.fl_str_mv en
eng
dc.publisher.en.fl_str_mv Institute of Mathematical Statistics
dc.relation.ispartof.es.fl_str_mv Latin American Journal of Probability and Mathematical Statistics, 2019, 16: 1105-1128
dc.rights.license.none.fl_str_mv Licencia Creative Commons Atribución (CC - By 4.0)
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
dc.source.none.fl_str_mv reponame:COLIBRI
instname:Universidad de la República
instacron:Universidad de la República
dc.subject.en.fl_str_mv Fractional Brownian motion
Fractional Ornstein-Uhlenbeck process
Long memory processes.
dc.title.none.fl_str_mv Fractional iterated Ornstein-Uhlenbeck Processes
dc.type.es.fl_str_mv Artículo
dc.type.none.fl_str_mv info:eu-repo/semantics/article
dc.type.version.none.fl_str_mv info:eu-repo/semantics/publishedVersion
description We present a Gaussian process that arises from the iteration of p fractional Ornstein–Uhlenbeck processes generated by the same fractional Brownian motion. When the values of the parameters defining the iteration are pairwise distinct, this iteration results in a particular linear combination of those processes. Although for H > 1=2 each term of the iteration is a long memory process, we prove that when p 2 the process obtained has short memory. We prove that the local Hölder index of the process is H, and obtain an explicit formula for the spectral density. We present a way to estimate the parameters and prove that the estimators are consistent and the results are asymptotically Gaussian. These processes can be used to model time series of long or short memory.
eu_rights_str_mv openAccess
format article
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identifier_str_mv Kalemkerian, J y León, J. "Fractional iterated Ornstein-Uhlenbeck Processes". Latin American Journal of Probability and Mathematical Statistics. [en línea] 2019, 16: 1105-1128. 24 h. DOI: 10.30757/ALEA.v.16-41
1980-0436
10.30757/ALEA.v16-41
instacron_str Universidad de la República
institution Universidad de la República
instname_str Universidad de la República
language eng
language_invalid_str_mv en
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publishDate 2019
reponame_str COLIBRI
repository.mail.fl_str_mv mabel.seroubian@seciu.edu.uy
repository.name.fl_str_mv COLIBRI - Universidad de la República
repository_id_str 4771
rights_invalid_str_mv Licencia Creative Commons Atribución (CC - By 4.0)
spelling Kalemkerian Juan, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.León José Rafael, Universidad de la República (Uruguay). Facultad de Ingeniería2021-07-07T14:40:29Z2021-07-07T14:40:29Z2019Kalemkerian, J y León, J. "Fractional iterated Ornstein-Uhlenbeck Processes". Latin American Journal of Probability and Mathematical Statistics. [en línea] 2019, 16: 1105-1128. 24 h. DOI: 10.30757/ALEA.v.16-411980-0436https://hdl.handle.net/20.500.12008/2848610.30757/ALEA.v16-41We present a Gaussian process that arises from the iteration of p fractional Ornstein–Uhlenbeck processes generated by the same fractional Brownian motion. When the values of the parameters defining the iteration are pairwise distinct, this iteration results in a particular linear combination of those processes. Although for H > 1=2 each term of the iteration is a long memory process, we prove that when p 2 the process obtained has short memory. We prove that the local Hölder index of the process is H, and obtain an explicit formula for the spectral density. We present a way to estimate the parameters and prove that the estimators are consistent and the results are asymptotically Gaussian. These processes can be used to model time series of long or short memory.Submitted by Verdun Juan Pablo (jverdun@fcien.edu.uy) on 2021-06-17T00:22:56Z No. of bitstreams: 2 license_rdf: 19875 bytes, checksum: 9fdbed07f52437945402c4e70fa4773e (MD5) 10.30757ALEA.v16-41.pdf: 730054 bytes, checksum: fe985e0d06e0ac3bcb4fd06d6a40493c (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2021-07-07T14:05:41Z (GMT) No. of bitstreams: 2 license_rdf: 19875 bytes, checksum: 9fdbed07f52437945402c4e70fa4773e (MD5) 10.30757ALEA.v16-41.pdf: 730054 bytes, checksum: fe985e0d06e0ac3bcb4fd06d6a40493c (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2021-07-07T14:40:29Z (GMT). No. of bitstreams: 2 license_rdf: 19875 bytes, checksum: 9fdbed07f52437945402c4e70fa4773e (MD5) 10.30757ALEA.v16-41.pdf: 730054 bytes, checksum: fe985e0d06e0ac3bcb4fd06d6a40493c (MD5) Previous issue date: 201924 h.application/pdfenengInstitute of Mathematical StatisticsLatin American Journal of Probability and Mathematical Statistics, 2019, 16: 1105-1128Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución (CC - By 4.0)Fractional Brownian motionFractional Ornstein-Uhlenbeck processLong memory processes.Fractional iterated Ornstein-Uhlenbeck ProcessesArtículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaKalemkerian, JuanLeón, José RafaelLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/28486/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-844http://localhost:8080/xmlui/bitstream/20.500.12008/28486/2/license_urla0ebbeafb9d2ec7cbb19d7137ebc392cMD52license_textlicense_texttext/html; charset=utf-838395http://localhost:8080/xmlui/bitstream/20.500.12008/28486/3/license_textd606c60c5d78967c4ed7a729e5bb402fMD53license_rdflicense_rdfapplication/rdf+xml; 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- Universidad de la Repúblicafalse
spellingShingle Fractional iterated Ornstein-Uhlenbeck Processes
Kalemkerian, Juan
Fractional Brownian motion
Fractional Ornstein-Uhlenbeck process
Long memory processes.
status_str publishedVersion
title Fractional iterated Ornstein-Uhlenbeck Processes
title_full Fractional iterated Ornstein-Uhlenbeck Processes
title_fullStr Fractional iterated Ornstein-Uhlenbeck Processes
title_full_unstemmed Fractional iterated Ornstein-Uhlenbeck Processes
title_short Fractional iterated Ornstein-Uhlenbeck Processes
title_sort Fractional iterated Ornstein-Uhlenbeck Processes
topic Fractional Brownian motion
Fractional Ornstein-Uhlenbeck process
Long memory processes.
url https://hdl.handle.net/20.500.12008/28486