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

E. Serrano and A. Figliola

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 14, 2793-2805

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.

Keywords: Wavelet Leaders; Multifractal formalism; Hölder regularity; Scalar invariance; Multifractal Detrended Fluctuation Analysis (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (14)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:14:p:2793-2805

DOI: 10.1016/j.physa.2009.03.043

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