Estimators of Long-Memory: Fourier versus Wavelets

Gilles Fay (1) , Éric Moulines (2) , François Roueff (2) , Murad S. Taqqu (3)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 LTCI - Laboratoire Traitement et Communication de l'Information
3 BU - Boston University [Boston]

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 illustrate its use at the end of the paper.

Mots clés: Wavelet analysis; long range dependence; semi-parametric estimation

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

Gilles Fay, Éric Moulines, François Roueff, Murad S. Taqqu. Estimators of Long-Memory: Fourier versus Wavelets. Econometrics, 2009, 151 (2), pp.159-177. ⟨10.1016/j.jeconom.2009.03.005⟩. ⟨hal-00221292⟩