Multifractal detrended cross-correlation analysis for two nonstationary signals

TL;DR

This paper introduces MF-DXA, a novel method for analyzing multifractal cross-correlations in nonstationary signals across multiple dimensions, validated with synthetic data and applied to financial time series.

Contribution

The paper presents a new multifractal detrended cross-correlation analysis method capable of handling nonstationary signals in multiple dimensions, extending existing techniques.

Findings

Validated with synthetic multifractal measures

Effectively captures multifractal cross-correlations

Applied successfully to financial data

Abstract

It is ubiquitous in natural and social sciences that two variables, recorded temporally or spatially in a complex system, are cross-correlated and possess multifractal features. We propose a new method called multifractal detrended cross-correlation analysis (MF-DXA) to investigate the multifractal behaviors in the power-law cross-correlations between two records in one or higher dimensions. The method is validated with cross-correlated 1D and 2D binomial measures and multifractal random walks. Application to two financial time series is also illustrated.