Journal
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
Volume 473, Issue -, Pages 467-487Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physa.2017.01.041
Keywords
Multifractal analysis; Multifractal moment method; Multifractal histogram method; Multifractal detrended fluctuation analysis; Multifractal modulus maxima wavelet transform method
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Funding
- ERC Grant [249393-ERC-2009-AdG]
- EPSRC Digital Economy Phase 2: UK Regions Digital Research Facility (UK RDRF) [EP/M023583/1]
- UK ESRC Consumer Data Research Centre (CDRC) [ES/L011840/1]
- EPSRC [EP/M023583/1] Funding Source: UKRI
- ESRC [ES/L011840/1] Funding Source: UKRI
- Economic and Social Research Council [ES/L011840/1] Funding Source: researchfish
- Engineering and Physical Sciences Research Council [EP/M023583/1] Funding Source: researchfish
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Various methods have been developed independently to study the multifractality of measures in many different contexts. Although they all convey the same intuitive idea of giving a dimension to sets where a quantity scales similarly within a space, they are not necessarily equivalent on a more rigorous level. This review article, aims at unifying the multifractal methodology by presenting the multifractal theoretical framework and principal practical methods, namely the moment method, the histogram method, multifractal detrended fluctuation analysis (MDFA) and wavelet transform modulus maxima (WTMM), with a comparative and interpretative eye. (C) 2017 The Authors. Published by Elsevier B.V.
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