Modelling a continuous time series with FOU(p) processes
Resumen:
In this work we summarize the knowledge about FOU(p) processes (fractional iterated Ornstein–Uhlenbeck processes of order emphp). Fractional Ornstein–Uhlenbeck processes are a particular case of FOU(p) processes (when p = 1). FOU(p) processes are able to model time series with both long- and short-range dependence. We give the definition, the main theoretical properties, and a procedure for estimating the parameters consistently. We also show how to model a continuous time series with FOU(p) processes, and we give an example of an application.
| 2022 | |
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Fractional Brownian motion; Long-range dependence Fractional Ornstein–Uhlenbeck process |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/41085 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| Sumario: | In this work we summarize the knowledge about FOU(p) processes (fractional iterated Ornstein–Uhlenbeck processes of order emphp). Fractional Ornstein–Uhlenbeck processes are a particular case of FOU(p) processes (when p = 1). FOU(p) processes are able to model time series with both long- and short-range dependence. We give the definition, the main theoretical properties, and a procedure for estimating the parameters consistently. We also show how to model a continuous time series with FOU(p) processes, and we give an example of an application. |
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