A new estimator for LARCH processes

Abstract

The aim of this article is to provide a new estimator of parameters for LARCH$\left(\infty \right)$ processes, and thus also for LARCH$\left(p\right)$ or GLARCH$(p,q)$ processes. This estimator results from minimizing 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.