A new semi-parametric estimator for LARCH processes

This paper aims at providing a new semi-parametric estimator for LARCH($\infty$) processes, and therefore also for LARCH(p) or GLARCH(p, q) processes. This estimator is obtained from the minimization of a contrast leading to a least squares estimator of the absolute values of the process. The strong consistency and the asymptotic normality are showed, and the convergence happens with rate $\sqrt$ n as well in cases of short or long memory. Numerical experiments confirm the theoretical results, and show that this new estimator clearly outperforms the smoothed quasi-maximum likelihood estimators or the weighted least square estimators often used for such processes.