Moment estimator for an AR(1) model with non-zero mean driven by a long memory Gaussian noise

TL;DR

This paper develops moment estimators for an AR(1) model with non-zero mean driven by long memory Gaussian noise, establishing their strong consistency and asymptotic properties.

Contribution

It introduces novel moment estimators for AR(1) models with long memory Gaussian noise and proves their consistency and asymptotic normality.

Findings

Proposed estimators are strongly consistent.

Establish asymptotic normality of the estimators.

Applicable to fractional Gaussian noise and fractional ARIMA models.

Abstract

In this paper, we consider an inference problem for the first order autoregressive process with non-zero mean driven by a long memory stationary Gaussian process. Suppose that the covariance function of the noise can be expressed as $|k|^{2H-2}$ times a positive constant when $k$ tends to infinity, and the fractional Gaussian noise and the fractional ARIMA model are special examples that satisfy this assumption. We propose moment estimators and prove the strong consistency, the asymptotic normality and joint asymptotic normality.