Adaptive wavelet based estimator of the memory 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

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.

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

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jean-Marc Bardet, Hatem Bibi, Abdellatif Jouini. Adaptive wavelet based estimator of the memory parameter for stationary Gaussian processes. Bernoulli, 2008, 14 (3), pp.691-724. ⟨10.3150/07-BEJ6151⟩. ⟨hal-00126756v2⟩