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What is Learnable in Valiant's Theory of the Learnable? 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A new estimator for LARCH processes
2021-10-25 · via math.ST updates on arXiv.org

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.

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