| Title: | A construction of continuous-time ARMA models by iterations of Ornstein-Uhlenbeck processes |
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| Author: | Arratia, Argimiro; Cabaña Nigro, Alejandra; Cabaña, Enrique M. |
| 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. |
| Subject(s): | -Ornstein-Uhlenbeck process -Lévy process -Continuous arma -Stationary process |
| Rights: | open access
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| Document type: | Article |
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| Uri: | https://ddd.uab.cat/record/168850 |
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