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Pre-averaging fractional processes contaminated by noise, with an application to turbulence

Year: 2025

Type: article

Abstract: 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.

Source: Journal of Applied Probability

DOI: 10.1017/jpr.2025.9

Authors: David Chen, Yu Cheng, Carsten H. Chong, Pierre Gentine, Wangdong Jia, Bryce J. Monier, Shiyang Shen

Institutions: University of Chicago, Harvard University, Hong Kong University of Science and Technology, Columbia University, University of California, Berkeley, California Institute of Technology

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

OpenAlex ID: W4416466289

FWCI: 1.948

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Cited by: 3

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