Maximum likelihood estimators and random walks in long memory models

TL;DR

This paper develops maximum likelihood estimators for drift parameters in long memory models driven by self-similar processes, using random walk approximations, and analyzes their asymptotic properties with supporting simulations.

Contribution

It introduces a novel approach to estimate parameters in long memory models via random walk approximations of the noise.

Findings

MLEs are consistent and asymptotically normal

Simulation results support theoretical findings

Method applies to Gaussian and non-Gaussian processes

Abstract

We consider statistical models driven by Gaussian and non-Gaussian self-similar processes with long memory and we construct maximum likelihood estimators (MLE) for the drift parameter. Our approach is based on the approximation by random walks of the driving noise. We study the asymptotic behavior of the estimators and we give some numerical simulations to illustrate our results.