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Wavelet Leaders: A new method to estimate the multifractal singularity spectra

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  • Serrano, E.
  • Figliola, A.

Abstract

Wavelet Leaders is a novel alternative based on wavelet analysis for estimating the Multifractal Spectrum. It was proposed by Jaffard and co-workers improving the usual wavelet methods. In this work, we analyze and compare it with the well known Multifractal Detrended Fluctuation Analysis. The latter is a comprehensible and well adapted method for natural and weakly stationary signals. Alternatively, Wavelet Leaders exploits the wavelet self-similarity structures combined with the Multiresolution Analysis scheme. We give a brief introduction on the multifractal formalism and the particular implementation of the above methods and we compare their effectiveness. We expose several cases: Cantor measures, Binomial Multiplicative Cascades and also natural series from a tonic–clonic epileptic seizure. We analyze the results and extract the conclusions.

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  • Serrano, E. & Figliola, A., 2009. "Wavelet Leaders: A new method to estimate the multifractal singularity spectra," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2793-2805.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:14:p:2793-2805
    DOI: 10.1016/j.physa.2009.03.043
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