Título:
Fractional iterated Ornstein-Uhlenbeck Processes
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Autor:
Kalemkerian, Juan
León, José Rafael
León, José Rafael
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Tipo de documento:
Artículo
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Palabras clave:
Fractional Brownian motion
Fractional Ornstein-Uhlenbeck process
Long memory processes.
Fractional Ornstein-Uhlenbeck process
Long memory processes.
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Año de publicación:
2019
Contenido:
Resumen:
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.
Descripción:
Editorial:
Institute of Mathematical Statistics
EN:
Latin American Journal of Probability and Mathematical Statistics, 2019, 16: 1105-1128
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Citación:
Kalemkerian, J y León, J. "Fractional iterated Ornstein-Uhlenbeck Processes". Latin American Journal of Probability and Mathematical Statistics. [en línea] 2019, 16: 1105-1128. 24 h. DOI: 10.30757/ALEA.v.16-41
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URI:
https://hdl.handle.net/20.500.12008/28486
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ISSN:
1980-0436
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Licencia Creative Commons Atribución (CC - By 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| 10.30757ALEA.v16-41.pdf | — | 712.94 KB | Adobe PDF |