A new estimator for LARCH processes

TL;DR

This paper introduces a novel least squares estimator for LARCH processes that is strongly consistent, asymptotically normal, and outperforms existing methods in numerical experiments.

Contribution

It proposes a new estimator based on a contrast minimization approach for LARCH processes, with proven theoretical properties and superior empirical performance.

Findings

Estimator is strongly consistent and asymptotically normal.

Convergence rate is √n in both short and long memory cases.

Numerical results show significant improvement over existing estimators.

Abstract

The aim of this paper is to provide a new estimator of parameters for LARCH$(\infty)$ processes, and thus also for LARCH$(p)$ or GLARCH$(p,q)$ processes. This estimator results from minimising a contrast leading to a least squares estimator for the absolute values of the process. Strong consistency and asymptotic normality are shown, and convergence occurs at the rate $\sqrt n$ as well in short or long memory cases. Numerical experiments confirm the theoretical results and show that this new estimator significantly outperforms the smoothed quasi-maximum likelihood estimators or weighted least squares estimators commonly used for such processes.