Wavelet transform modulus maxima based fractal correlation analysis

TL;DR

This paper extends the wavelet transform modulus maxima method to analyze the fractal correlation between two multifractal functions, integrating it within the joint partition function analysis framework and relating it to relative multifractal analysis.

Contribution

It introduces a novel extension of WTMM for fractal correlation analysis and connects it with existing multifractal analysis methods.

Findings

WTMM effectively analyzes fractal correlation between multifractal functions.

JPFA framework can incorporate WTMM for joint analysis.

Relative multifractal analysis is a special case of JPFA.

Abstract

The wavelet transform modulus maxima (WTMM) used in the singularity analysis of one fractal function is extended to study the fractal correlation of two multifractal functions. The technique is developed in the framework of joint partition function analysis (JPFA) proposed by Meneveau et al. [1] and is shown to be equally effective. In addition, we show that another leading approach developed for the same purpose, namely, relative multifractal analysis, can be considered as a special case of JPFA at a particular parameter setting.