Modified wavelet variation for the Hermite processes
Statistics Theory
2024-03-11 v1 Probability
Statistics Theory
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.
Cite
@article{arxiv.2403.05140,
title = {Modified wavelet variation for the Hermite processes},
author = {Laurent Loosveldt and Ciprian A. Tudor},
journal= {arXiv preprint arXiv:2403.05140},
year = {2024}
}