Open Access
2023 Estimation of the Hurst parameter from continuous noisy data
Pavel Chigansky, Marina Kleptsyna
Author Affiliations +
Electron. J. Statist. 17(2): 2343-2385 (2023). DOI: 10.1214/23-EJS2156


This paper addresses the problem of estimating the Hurst exponent of the fractional Brownian motion from continuous time noisy sample. When the Hurst parameter is greater than 34, consistent estimation is possible only if either the length of the observation interval increases to infinity or intensity of the noise decreases to zero. The main result is a proof of the Local Asymptotic Normality (LAN) of the model in these two regimes which reveals the optimal minimax estimation rates.

Funding Statement

Pavel Chigansky was supported by ISF 1383/18 grant. Marina Kleptsyna was supported by ANR EFFI grant.


Download Citation

Pavel Chigansky. Marina Kleptsyna. "Estimation of the Hurst parameter from continuous noisy data." Electron. J. Statist. 17 (2) 2343 - 2385, 2023.


Received: 1 June 2022; Published: 2023
First available in Project Euclid: 4 October 2023

arXiv: 2205.11092
MathSciNet: MR4649984
Digital Object Identifier: 10.1214/23-EJS2156

Primary: 60G22 , 62F12

Keywords: fractional Brownian motion , Hurst parameter estimation , local asymptotic normality

Vol.17 • No. 2 • 2023
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