Work

Optimal estimation of the rough Hurst parameter in additive noise

Year: 2024

Type: article

Abstract: We estimate the Hurst parameter H∈(0,1) of a fractional Brownian motion from discrete noisy data, observed along a high-frequency sampling scheme. When the intensity τn of the noise is smaller in order than n−H we establish the LAN property with optimal rate n−1/2. Otherwise, we establish that the minimax rate of convergence is (n/τn2)−1/(4H+2) even when τn is of order 1. Our construction of an optimal procedure relies on a Whittle type construction possibly pre-averaged, together with techniques developed in Fukasawa et al. (2019). We establish in all cases a central limit theorem with explicit variance, extending the classical results of Gloter and Hoffmann (2007).

Source: Stochastic Processes and their Applications

DOI: 10.1016/j.spa.2024.104302

Author: Grégoire Szymanski

Institution: École Polytechnique

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,420

OpenAlex ID: W4391071632

FWCI: 2.563

Cites: 38

Cited by: 14

Related to: 10