Modelling a continuous time series with FOU(p) processes

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

An optimal aggregation type classifier

We introduce a nonlinear aggregation type classifier for functional data defined on a separable and complete metric space. The new rule is built up from a collection of $M$ arbitrary training classifiers. If the classifiers are consistent, then so is the aggregation rule. Moreover, asymptotically the aggregation rule behaves as well as the best of the $M$ classifiers. The results of a small si\-mu\-lation are reported both, for high dimensional and functional data

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 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

Prediction using ARFIMA and FOU models of affluent energy

En este trabajo se estudian predicciones a partir de modelos ARFIMA y FOU para la serie de datos semanales de energía afluente generada por las represas hidroeléctricas de Uruguay entre 1909 y 2012. Se describe la serie de datos, y mediante la estimación del exponente de Hurst se muestra la conveniencia de modelar a través de procesos de memoria larga. Se presentan dos familias de modelos de series de tiempo de este tipo, los ARFIMA y los FOU (Ornstein-Uhlenbeck fraccionarios). Se estiman sus parámetros y se compara el rendimiento de los mismos teniendo en cuenta su poder predictivo.In this work we study predictions from ARFIMA and FOU models for the weekly data series of affluent energy generated by hydroelectric dams in Uruguay between 1909 and 2012. The estimation of Hurst coefficient suggests modeling through long memory time series. We present two families of time series models of this type, ARFIMA and FOU (fractional Ornstein-Uhlenbeck) models. Their parameters are estimated and taking into account their predictive power, their performance is compared