Non-parametric estimation of the long-range dependence exponent for Gaussian processes

We consider a class of long-range-dependent Gaussian processes defined in a semiparametric framework. We propose a new estimator of the long-range dependence parameter, based on the integration of the periodogram in two windows. We show that it is asymptotically Gaussian and calculate the rate of convergence. We optimise parameters defining the window function for the minimum mean-square-error criterion. In a Monte-Carlo study, we compare the proposed estimator with previously studied estimators.