Asymptotic expansion of an estimator for the Hurst coefficient

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