Fractional iterated Ornstein-Uhlenbeck Processes

TL;DR

This paper introduces a new Gaussian process formed by iterating fractional Ornstein-Uhlenbeck processes driven by the same fractional Brownian motion, revealing short memory properties and demonstrating improved predictive performance over ARMA models.

Contribution

It presents a novel Gaussian process derived from iterated fractional Ornstein-Uhlenbeck processes, showing its short memory behavior despite long memory components.

Findings

The process exhibits short memory properties for H>1/2.

Application to real data improves predictive accuracy over ARMA models.

The linear combination of processes results in a process with distinct memory characteristics.

Abstract

In this work we present a Gaussian process that arise from the iteration of p fractional Ornstein-Uhlenbeck processes generated by the same fractional Brownian motion. This iteration results, when the values of lambdas are pairwise differents, in a particular linear combination of those processes. Although for $H>1/2$ each term of the linear combination is a long memory processes, we prove that it results in a short memory processes. We include applications to real data that show improvement in predictive performance compared with different ARMA models.