Quasi-Maximum Likelihood Estimation of long-memory linear processes

TL;DR

This paper investigates the convergence properties of the quasi-maximum likelihood estimator for long-memory linear processes, establishing consistency and asymptotic normality, supported by numerical simulations.

Contribution

It provides a theoretical foundation for the QML estimator's convergence in long-memory processes and links process representations.

Findings

QML estimator is consistent for long-memory processes

QML estimator is asymptotically normal

Numerical simulations confirm theoretical results

Abstract

The purpose of this paper is to study the convergence of the quasi-maximum likelihood (QML) estimator for long memory linear processes. We first establish a correspondence between the long-memory linear process representation and the long-memory AR$(\infty)$ process representation. We then establish the almost sure consistency and asymptotic normality of the QML estimator. Numerical simulations illustrate the theoretical results and confirm the good performance of the estimator.