Multifractal methodology
Hadrien Salat, Roberto Murcio, Elsa Arcaute
TL;DR
This paper reviews and unifies various multifractal analysis methods, providing a comprehensive theoretical framework and comparing practical techniques like the moment method, histogram method, MDFA, and MMWT.
Contribution
It offers a unified presentation of multifractal methodology, clarifying theoretical foundations and comparing key practical approaches.
Findings
Provides a comprehensive theoretical framework
Comparative analysis of practical multifractal methods
Clarifies the equivalences and differences among methods
Abstract
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 modulus maxima wavelet transform (MMWT), with a comparative and interpretative eye.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.