Joint multifractal analysis based on wavelet leaders

TL;DR

This paper introduces a novel wavelet leader-based method for analyzing joint multifractal properties of long-range cross-correlated systems, validated through numerical experiments and real-world data applications.

Contribution

It proposes the MF-X-WL method for characterizing joint multifractality, demonstrating its effectiveness in synthetic and real-world datasets.

Findings

MF-X-WL accurately detects cross correlations in synthetic data.

The method reveals joint multifractal behavior in financial and online data.

It performs with acceptable estimation errors in tests.

Abstract

Mutually interacting components form complex systems and the outputs of these components are usually long-range cross-correlated. Using wavelet leaders, we propose a method of characterizing the joint multifractal nature of these long-range cross correlations, a method we call joint multifractal analysis based on wavelet leaders (MF-X-WL). We test the validity of the MF-X-WL method by performing extensive numerical experiments on the dual binomial measures with multifractal cross correlations and the bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. Both experiments indicate that MF-X-WL is capable to detect the cross correlations in synthetic data with acceptable estimating errors. We also apply the MF-X-WL method to the pairs of series from financial markets (returns and volatilities) and online worlds (online numbers of different genders and different societies) and find an intriguing joint multifractal behavior.