Pre-averaging fractional processes contaminated by noise, with an application to turbulence
Statistics Theory
2026-01-14 v1 Applications
Statistics Theory
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.
Keywords
Cite
@article{arxiv.2212.00867,
title = {Pre-averaging fractional processes contaminated by noise, with an application to turbulence},
author = {David Chen and Yu Cheng and Carsten Chong and Pierre Gentine and Wangdong Jia and Bryce Monier and Shiyang Shen},
journal= {arXiv preprint arXiv:2212.00867},
year = {2026}
}