A new estimator for LARCH processes

Abstract

The aim of this article is to provide a new estimator of parameters for LARCH processes, and thus also for LARCH or GLARCH 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 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.