Asymptotic expansion of an estimator for the Hurst coefficient

Abstract

AbstractAsymptotic 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.