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Issue ESAIM: Proc.
Volume 5, 1998
Fractional Differential Systems: Models, Methods and Applications
Page(s) 29 - 41
DOI http://dx.doi.org/10.1051/proc:1998010

ESAIM: Proc., 1998, Vol. 5, pp. 29-41
DOI: 10.1051/proc:1998010

Recent advances on the semi-parametric estimation of the long-range dependence coefficient

Jean-Marc Bardet1, Éric Moulines2 and Philippe Soulier3

1  Université Paul Sabatier Toulouse III, Laboratoire de Statistiques et de Probabilités, 118 route de Narbonne, 31004 Toulouse Cedex, France
2  ENST/TSI & CNRS, URA 820, GdR ISIS, 46, rue Barrault, 75 634 Paris Cedex 13, France
3  Université d'Evry Val d'Essonne, Laboratoire de Mathématiques et d'Informatique, 91025 Evry Cedex, France


Abstract
Semi-parametric estimation of the long-range dependence parameter was a subject of major interest in recent years. The purpose of this paper is to put in a common framework several recent contributions of that topic. We will focus in particular on spectral methods, which consist in estimating the exponent of the singularity of the spectral density function at zero frequency and on time-domain methods, which are based on the estimation on the rate of convergence to zero of the autocovariance coefficients and/or on the scaling of the variance of processes deduced from the original process by generalized aggregation.



© EDP Sciences, ESAIM 1998


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