Fractional iterated Ornstein-Uhlenbeck Processes
We present a Gaussian process that arises from the iteration of p fractional Ornstein–Uhlenbeck processes generated by the same fractional Brownian motion. When the values of the parameters defining the iteration are pairwise distinct, this iteration results in a particular linear combination of tho...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | Uruguay |
| Institución: | Universidad de la República |
| Repositorio: | COLIBRI |
| Idioma: | inglés |
| OAI Identifier: | oai:colibri.udelar.edu.uy:20.500.12008/28486 |
| Acceso en línea: | https://hdl.handle.net/20.500.12008/28486 |
| Access Level: | acceso abierto |
| Palabra clave: | Fractional Brownian motion Fractional Ornstein-Uhlenbeck process Long memory processes. |
| Sumario: | We present a Gaussian process that arises from the iteration of p fractional Ornstein–Uhlenbeck processes generated by the same fractional Brownian motion. When the values of the parameters defining the iteration are pairwise distinct, this iteration results in a particular linear combination of those processes. Although for H > 1=2 each term of the iteration is a long memory process, we prove that when p 2 the process obtained has short memory. We prove that the local Hölder index of the process is H, and obtain an explicit formula for the spectral density. We present a way to estimate the parameters and prove that the estimators are consistent and the results are asymptotically Gaussian. These processes can be used to model time series of long or short memory. |
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