Adaptive wavelet based estimator of long-range dependence parameter for stationary Gaussian processes

Jean-Marc Bardet (1, 2) , Hatem Bibi (1, 2) , Abdellatif Jouini (3)

1 SAMOS - Statistique Appliquée et MOdélisation Stochastique
2 CES - Centre d'économie de la Sorbonne
3 DéPARTEMENT DE MATHéMATIQUES - Département de Mathématiques, Faculté des Sciences de

The aim of this contribution is to provide an adaptive estimation of the long-memory parameter in the classical semi-parametric framework for Gaussian stationary processes using a wavelet method. In particular, the choice of a data-driven optimal band of scales is introduced and developed. Moreover, a central limit theorem for the estimator of the long-memory parameter reaching the minimax rate of convergence (up to a logarithm factor) is established. Simulations confirm the quality of this estimator.

Mots clés: Adaptive estimator; Long-memory processes; Semi-parametric estimation; Wavelet analysis

Domaines: Statistiques [math.ST]

Jean-Marc Bardet, Hatem Bibi, Abdellatif Jouini. Adaptive wavelet based estimator of long-range dependence parameter for stationary Gaussian processes. 2007. ⟨hal-00126756v1⟩