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.

翻译：本文旨在研究长记忆线性过程的拟极大似然（QML）估计量的收敛性。我们首先建立长记忆线性过程表示与长记忆AR($\infty$)过程表示之间的对应关系，随后证明QML估计量的几乎必然一致性和渐近正态性。数值模拟结果验证了理论结论并证实了该估计量的良好性能。