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Asymptotic expansion of an estimator for the Hurst coefficient

Statistical Inference for Stochastic Processes : An International Journal devoted to Time Series Analysis and the Statistics of Continuous Time Processes and Dynamical Systems (SISP), 2022
Y. Mishura
Hayate Yamagishi
Nakahiro Yoshida
ArXiv (abs)PDFHTML
Abstract

Asymptotic expansion is presented for an estimator of the Hurst coefficient of a fractional Brownian motion. For this, a recently developed theory of asymptotic expansion of the distribution of Wiener functionals is applied. The effects of the asymptotic expansion are demonstrated by numerical studies.

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