A new semi-parametric estimator for LARCH processes

10/25/2021

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by   Jean-Marc Bardet, et al.

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This paper aims at providing a new semi-parametric estimator for LARCH(∞) 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 √($) 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.