Pre-averaging fractional processes contaminated by noise, with an application to turbulence
Abstract
In this article, we consider the problem of estimating fractional processes based on noisy high-frequency data. Generalizing the idea of pre-averaging to a fractional setting, we exhibit a sequence of consistent estimators for the unknown parameters of interest by proving a law of large numbers for associated variation functionals. In contrast to the semimartingale setting, the optimal window size for pre-averaging depends on the unknown roughness parameter of the underlying process. We evaluate the performance of our estimators in a simulation study and use them to empirically verify Kolmogorov's 2/3-law in turbulence data contaminated by instrument noise.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2022
- DOI:
- 10.48550/arXiv.2212.00867
- arXiv:
- arXiv:2212.00867
- Bibcode:
- 2022arXiv221200867C
- Keywords:
-
- Mathematics - Statistics Theory;
- Statistics - Applications;
- 60F25;
- 60G22;
- 62M09;
- 76M35;
- 62G05;
- 76F55