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

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

2007-01-26

arxiv.org/abs/math/0701770v2

Bernoulli 14, 2 (2008) xx-xx

Mathematics

Statistics Theory

Scientific paper

This work is intended as a contribution to 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 are attested by simulations.

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