Semi-parametric estimation of the long-range dependence parameter : A survey

Jean-Marc Bardet (1, 2) , Anne Philippe (3) , Georges Oppenheim (4) , Murad S. Taqqu (5) , Stilan Stoev (5) , Gabriel Lang (6)

1 SAMOS - Statistique Appliquée et MOdélisation Stochastique
2 MATISSE - UMR 8595 - Modélisation Appliquée, Trajectoires Institutionnelles et Stratégies Socio-Économiques
3 LPP - Laboratoire Paul Painlevé - UMR 8524
4 LM-Orsay - Laboratoire de Mathématiques d'Orsay
5 Department of Mathematics, Boston University
6 GRESE - Laboratoire de Gestion du Risque En Sciences de l'Environnement

In semi-parametric models, the long-range dependence parameter is estimated without assuming that the short-range dependence structure of the covariance function is known. We review some of the estimation methods and present new ones which have not been tested before on simulated data.

Mots clés: fractional Gaussian noise; self-similarity; time series; FARIMA; estimation

Domaines: Statistiques [math.ST]

Jean-Marc Bardet, Anne Philippe, Georges Oppenheim, Murad S. Taqqu, Stilan Stoev, et al.. Semi-parametric estimation of the long-range dependence parameter : A survey. Theory and applications of long-range dependence., Birkhäuser, pp.557-577, 2003. ⟨hal-00127926⟩