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Estimators of Long-Memory: Fourier versus Wavelets
Faÿ G., Moulines E., Roueff F., Taqqu M.S.
Journal of Econometrics 151 (2009) 159-177 - http://hal.in2p3.fr/in2p3-00185534
Mathématiques/Statistiques
Statistiques/Théorie
Estimators of Long-Memory: Fourier versus Wavelets
G. Faÿ1, 2, E. Moulines, F. Roueff, M.S. Taqqu
1 :  APC - UMR 7164 - AstroParticule et Cosmologie
http://www.apc.univ-paris7.fr/
CNRS : UMR7164 – IN2P3 – Observatoire de Paris – Université Paris VII - Paris Diderot – CEA : DSM/IRFU
APC - UMR 7164, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, case postale 7020, F-75205 Paris Cedex 13
France
2 :  LPP - Laboratoire Paul Painlevé
http://math.univ-lille1.fr/
CNRS : UMR8524 – Université Lille I - Sciences et technologies
U.F.R. de Mathématiques 59 655 Villeneuve d'Ascq Cédex
France
APC - ADAMIS
There have been a number of papers written on semi-parametric estimation methods of the long-memory exponent of a time series, some applied, others theoretical. Some using Fourier methods, others using a wavelet-based technique. In this paper, we compare the Fourier and wavelet approaches to the local regression method and to the local Whittle method. We provide an overview of these methods, describe what has been done, indicate the available results and the conditions under which they hold. We discuss their relative strengths and weaknesses both from a practical and a theoretical perspective. We also include a simulation-based comparison. The software written to support this work is available on demand and we describe its use in the appendix.

Articles dans des revues avec comité de lecture
2009
Journal of Econometrics
Publisher Elsevier
ISSN 0304-4076 
151
159-177