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.
Funder
Core Research for Evolutional Science and Technology
Japan Society for the Promotion of Science
Institute of Statistical Mathematics
Stiftelsen för Strategisk Forskning
Publisher
Springer Science and Business Media LLC
Subject
Statistics and Probability