A construction of continuous-time ARMA models by iterations of Ornstein-Uhlenbeck processes
Arratia, Argimiro (Universitat Politècnica de Catalunya. Departament de Llenguatges i Sistemes Informàtics)
Cabaña Nigro, Alejandra (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Cabaña, Enrique M. (Universidad de la República (Montevideo, Uruguai))

Date: 2016
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 Lévy 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.
Rights: Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades. Creative Commons
Language: Anglès.
Document: article ; recerca ; publishedVersion
Subject: Ornstein-Uhlenbeck process ; Lévy process ; Continuous arma ; Stationary process
Published in: SORT : statistics and operations research transactions, Vol. 40 Núm. 2 (July-December 2016) , p. 267-302 (Articles) , ISSN 1696-2281

Adreça original: https://www.raco.cat/index.php/SORT/article/view/316146


36 p, 1.9 MB

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Articles > Published articles > SORT
Articles > Research articles

 Record created 2017-01-10, last modified 2019-02-05



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