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Journal Articles Econometrics Year : 2009

Estimators of Long-Memory: Fourier versus Wavelets

G. Faÿ
  • Function : Author
E. Moulines
François Roueff
M.S. Taqqu
  • Function : Author


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.

Dates and versions

in2p3-00185534 , version 1 (06-11-2007)



G. Faÿ, E. Moulines, François Roueff, M.S. Taqqu. Estimators of Long-Memory: Fourier versus Wavelets. Econometrics, 2009, 151, pp.159-177. ⟨10.1016/j.jeconom.2009.03.005⟩. ⟨in2p3-00185534⟩
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