Multifractal Height Cross-Correlation Analysis: A New Method for Analyzing Long-Range Cross-Correlations

TL;DR

This paper presents MF-HXA, a novel method for detecting long-range cross-correlations and multifractality in paired time series, extending previous height-height correlation analysis to a bivariate context.

Contribution

The paper introduces MF-HXA, a new bivariate multifractal analysis technique based on qth order covariances, capable of analyzing long-range cross-correlations.

Findings

Successfully applied to simulated data demonstrating accuracy.

Effectively used on real-world data showing practical relevance.

Revealed multifractal cross-correlations in empirical series.

Abstract

We introduce a new method for detection of long-range cross-correlations and multifractality - multifractal height cross-correlation analysis (MF-HXA) - based on scaling of qth order covariances. MF-HXA is a bivariate generalization of the height-height correlation analysis of Barabasi & Vicsek [Barabasi, A.L., Vicsek, T.: Multifractality of self-affine fractals, Physical Review A 44(4), 1991]. The method can be used to analyze long-range cross-correlations and multifractality between two simultaneously recorded series. We illustrate a power of the method on both simulated and real-world time series.