Modelling a continuous time series with FOU(p) processes

Abstract

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.