Modified wavelet variation for the Hermite processes
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2024
- DOI:
- 10.48550/arXiv.2403.05140
- arXiv:
- arXiv:2403.05140
- Bibcode:
- 2024arXiv240305140L
- Keywords:
-
- Mathematics - Statistics Theory;
- Mathematics - Probability;
- 60G18;
- 60H05;
- 60H07;
- 62F12;
- 60F05. 60G18;
- 60H05;
- 60H07;
- 62F12;
- 60F05. 60G18;
- 60H05;
- 60H07;
- 62F12;
- 60F05