Revistes Publicacions URV: SORT - Statistics and Operations Research Transactions> 2016

A construction of continuous-time ARMA models by iterations of Ornstein-Uhlenbeck processes

  • Identification data

    Identifier: RP:2448
    Handle: https://hdl.handle.net/20.500.11797/RP2448
    Authors:
    Cabaña, Enrique M.Cabaña, AlejandraArratia, Argimiro
    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.

  • Others:

    URV's Author/s: Cabaña, Enrique M. Cabaña, Alejandra Arratia, Argimiro
    Keywords: Ornstein-Uhlenbeck process, Lévy process, Continuous ARMA, stationary process
    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.
    Journal publication year: 2016
    Publication Type: info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article

  • Keywords:

    Ornstein-Uhlenbeck process, Lévy process, Continuous ARMA, stationary process

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