Fractional iterated Ornstein-Uhlenbeck Processes
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.
2019 | |
Fractional Brownian motion Fractional Ornstein-Uhlenbeck process Long memory processes. |
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Inglés | |
Universidad de la República | |
COLIBRI | |
https://hdl.handle.net/20.500.12008/28486 | |
Acceso abierto | |
Licencia Creative Commons Atribución (CC - By 4.0) |
_version_ | 1807522786704359424 |
---|---|
author | Kalemkerian, Juan |
author2 | León, José Rafael |
author2_role | author |
author_facet | Kalemkerian, Juan León, José Rafael |
author_role | author |
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bitstream.checksumAlgorithm.fl_str_mv | MD5 MD5 MD5 MD5 MD5 |
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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 |
id | COLIBRI_5a1d234854cbc3229304a596b7d66fbb |
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 |
network_acronym_str | COLIBRI |
network_name_str | COLIBRI |
oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/28486 |
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 |