Adaptive wavelet-based estimator of the memory parameter for stationary Gaussian processes

Abstract

This work is intended as a contribution to the theory of a wavelet-based adaptive estimator of the memory parameter in the classical semi-parametric framework for Gaussian stationary processes. In particular, we introduce and develop the choice of a data-driven optimal bandwidth. Moreover, we establish a central limit theorem for the estimator of the memory parameter with the minimax rate of convergence (up to a logarithm factor). The quality of the estimators is demonstrated via simulations.