Statistical Inference in Fractional Poisson Ornstein-Uhlenbeck Process

TL;DR

This paper investigates parameter estimation methods for a fractional Poisson-driven Ornstein-Uhlenbeck process, analyzing their asymptotic properties and validating findings through simulations.

Contribution

It introduces estimation techniques for a Poisson fractional Ornstein-Uhlenbeck process and studies their asymptotic behavior, which is a novel application in this context.

Findings

Asymptotic properties of estimators are established.

Simulation results support theoretical findings.

Abstract

In this article, we study the problem of parameter estimation for a discrete Ornstein - Uhlenbeck model driven by Poisson fractional noise. Based on random walk approximation for the noise, we study least squares and maximum likelihood estimators. Thus, asymptotic behaviours of the estimator is carried out, and a simulation study is shown to illustrate our results.