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Adaptive wavelet based estimator of the memory parameter for stationary Gaussian processes

Jean-Marc Bardet·Hatem Bibi·Abdellatif Jouini
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Abstract

This work is intended as a contribution to a wavelet-based adaptive estimator of the memory parameter in the classical semi-parametric framework for Gaussian stationary processes. In particular we introduce and develop the choice of a data-driven optimal bandwidth. Moreover, we establish a central limit theorem for the estimator of the memory parameter with the minimax rate of convergence (up to a logarithm factor). The quality of the estimators are attested by simulations.

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Jean-Marc Bardet, Hatem Bibi, Abdellatif Jouini. 2008-02-04. Adaptive wavelet based estimator of the memory parameter for stationary Gaussian processes. https://arxiv.org/abs/math/0701770

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