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A construction of continuous-time ARMA models by iterations of Ornstein-Uhlenbeck processes
dc.contributor.author | Arratia Quesada, Argimiro Alejandro |
dc.contributor.author | Cabaña, Ana Alejandra |
dc.contributor.author | Cabaña Perez, Enrique |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Ciències de la Computació |
dc.date.accessioned | 2017-03-08T09:17:40Z |
dc.date.available | 2017-03-08T09:17:40Z |
dc.date.issued | 2016-12 |
dc.identifier.citation | Arratia, A., Cabaña, A., Cabaña, E. M. A construction of continuous-time ARMA models by iterations of Ornstein-Uhlenbeck processes. "SORT: statistics and operations research transactions", Desembre 2016, vol. 40, núm. 2, p. 267-302. |
dc.identifier.issn | 1696-2281 |
dc.identifier.uri | http://hdl.handle.net/2117/102108 |
dc.description.abstract | We present a construction of a family of continuous-time ARMA processes based on p iterations of the linear operator that maps a Lévy process onto an Ornstein-Uhlenbeck process. The construction resembles the procedure to build an AR(p) from an AR(1). We show that this family is in fact a subfamily of the well-known CARMA(p,q) processes, with several interesting advantages, including a smaller number of parameters. The resulting processes are linear combinations of Ornstein-Uhlenbeck processes all driven by the same L´evy process. This provides a straightforward computation of covariances, a state-space model representation and methods for estimating parameters. Furthermore, the discrete and equally spaced sampling of the process turns to be an ARMA(p, p-1) process. We propose methods for estimating the parameters of the iterated Ornstein-Uhlenbeck process when the noise is either driven by a Wiener or a more general Lévy process, and show simulations and applications to real data. |
dc.format.extent | 36 p. |
dc.language.iso | eng |
dc.publisher | Institut d'Estadística de Catalunya |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.lcsh | Lévy processes |
dc.subject.lcsh | Ornstein-Uhlenbeck process |
dc.subject.lcsh | Stochastic processes |
dc.subject.other | Ornstein-Uhlenbeck process |
dc.subject.other | Lévy process |
dc.subject.other | Continuous ARMA |
dc.subject.other | Stationary process |
dc.title | A construction of continuous-time ARMA models by iterations of Ornstein-Uhlenbeck processes |
dc.type | Article |
dc.subject.lemac | Lévy, Processos de |
dc.subject.lemac | Processos estocàstics |
dc.contributor.group | Universitat Politècnica de Catalunya. LARCA - Laboratori d'Algorísmia Relacional, Complexitat i Aprenentatge |
dc.identifier.doi | 10.2436/20.8080.02.44 |
dc.description.peerreviewed | Peer Reviewed |
dc.relation.publisherversion | http://www.idescat.cat/sort/sort402/40.2.3.cabana-etal.pdf |
dc.rights.access | Open Access |
local.identifier.drac | 19738091 |
dc.description.version | Postprint (published version) |
local.citation.author | Arratia, A.; Cabaña, A.; Cabaña, E. M. |
local.citation.publicationName | SORT: statistics and operations research transactions |
local.citation.volume | 40 |
local.citation.number | 2 |
local.citation.startingPage | 267 |
local.citation.endingPage | 302 |
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