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Companion Webpage of the paper entitled "Multifractal Analysis based on Amplitude Extrema of Intrinsic Mode Functions", published in the Physical Review E ^†.

Abstract:

In this study, a Multifractal Formalism based on the Empirical Mode Decomposition is proposed. Scaling exponents are estimated from statistical moments computed over a discrete set of multiresolution parameters, namely, the dominant amplitude coefficients, which are selected among the local maxima observed across the set of envelopes of the Intrinsic Mode Functions.  Analyses of synthetic fractal and multifractal processes demonstrate that the proposed technique is capable of overcoming the negative moment divergence problem, and is competitive with other multifractal formalisms.

Computer program with examples of the EMD-DAMF method

Click here to download a  Zip or a Gzip Tarball package with (documented) Matlab® scripts associated with the simulations shown in the paper.

^†Soon after the article was published online we were informed by Dr. François Schmitt that the scaling exponents of Lévy walks [Equation (7)] were firstly derived in Schmitt, F., Schertzer, D., Lovejoy, S. (1999). Multifractal analysis of foreign exchange data. Applied Stochastic Models and Data Analysis, 15(1), 29-53. We would like to thank Dr. François Schmitt for pointing us this fact, and give credit to his original work.