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

  1. Argimiro Arratia 1
  2. Alejandra Cabaña 2
  3. Enrique M. Cabaña 3
  1. 1 Universitat Politècnica de Catalunya
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    Universitat Politècnica de Catalunya

    Barcelona, España

    ROR https://ror.org/03mb6wj31

  2. 2 Universitat Autònoma de Barcelona
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    Universitat Autònoma de Barcelona

    Barcelona, España

    ROR https://ror.org/052g8jq94

  3. 3 Universidad de la República
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    Universidad de la República

    Montevideo, Uruguay

    ROR https://ror.org/030bbe882

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Revista:
Sort: Statistics and Operations Research Transactions

ISSN: 1696-2281

Año de publicación: 2016

Volumen: 40

Número: 2

Páginas: 267-302

Tipo: Artículo

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Otras publicaciones en: Sort: Statistics and Operations Research Transactions

Resumen

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.

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Información de financiación

Supported by Spain's MINECO project APCOM (TIN2014-57226-P) and Generalitat de Catalunya 2014SGR 890 (MACDA). Supported by Spain's MINECO project MTM2015-69493-R.

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