Parameter estimation for the FOU(p) process with the same lambda

TL;DR

This paper introduces a new, efficient method for estimating the common lambda parameter in FOU(p) processes, demonstrating its effectiveness through simulations and real data applications, and comparing favorably to ARMA models.

Contribution

The paper proposes a novel, faster, and more efficient estimation method for the shared lambda in FOU(p) processes, with proven consistency and asymptotic normality.

Findings

The new method is more efficient than the general approach.

It performs well in simulations and real data.

It outperforms ARMA models in applications.

Abstract

The FOU(p) processes can be considered as an alternative to ARMA (or ARFIMA) processes to model time series. Also, there is no substantial loss when we model a time series using FOU(p) processes with the same lambda, than using differents values of lambda. In this work we propose a new method to estimate the unique value of lambda in a FOU(p) process. Under certain conditions, we will prove consistency and asymptotic normality. We will show that this new method is more easy and fast to compute. By simulations, we show that the new procedure work well and is more efficient than the general method. Also, we include an application to real data, and we show that the new method work well too and outperforms the family of ARMA(p, q).