Asymptotic expansion of an estimator for the Hurst coefficient

Yuliya Mishura (), Hayate Yamagishi () and Nakahiro Yoshida ()
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Yuliya Mishura: Taras Shevchenko National University of Kyiv
Hayate Yamagishi: The University of Tokyo
Nakahiro Yoshida: The University of Tokyo

Statistical Inference for Stochastic Processes, 2024, vol. 27, issue 1, No 6, 211 pages

Abstract: Abstract Asymptotic expansion is presented for an estimator of the Hurst coefficient of a fractional Brownian motion. We first derive the expansion formula of the principal term of the error of the estimator using a recently developed theory of asymptotic expansion of the distribution of Wiener functionals, and utilize the perturbation method on the obtained formula in order to calculate the expansion of the estimator. We also discuss some second-order modifications of the estimator. Numerical results show that the asymptotic expansion attains higher accuracy than the normal approximation.

Keywords: Asymptotic expansion; Hurst coefficient; Fractional Brownian motion; Malliavin calculus; Central limit theorem; Edgeworth expansion (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11203-023-09298-8

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