A construction of continuous-time ARMA models by iterations of Ornstein-Uhlenbeck processes
Tipus de documentArticle
EditorInstitut d'Estadística de Catalunya
Condicions d'accésAccés obert
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.
CitacióArratia, 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.
Versió de l'editorhttp://www.idescat.cat/sort/sort402/40.2.3.cabana-etal.pdf