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arXiv · 2403.05140

Modified wavelet variation for the Hermite processes

Laurent Loosveldt·Ciprian A. Tudor
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Abstract

We define an asymptotically normal wavelet-based strongly consistent estimator for the Hurst parameter of any Hermite processes. This estimator is obtained by considering a modified wavelet variation in which coefficients are wisely chosen to be, up to negligeable remainders, independent. We use Stein-Malliavin calculus to prove that this wavelet variation satisfies a multidimensional Central Limit Theorem, with an explicit bound for the Wasserstein distance.

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Laurent Loosveldt, Ciprian A. Tudor. 2024-03-08. Modified wavelet variation for the Hermite processes. https://arxiv.org/abs/2403.05140

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