Multifractal temporally weighted detrended partial cross-correlation analysis to quantify intrinsic power-law cross-correlation of two non-stationary time series affected by common external factors

TL;DR

This paper introduces MF-TWDPCCA, a novel method to accurately measure intrinsic power-law cross-correlations between non-stationary time series affected by external factors, improving analysis in complex systems.

Contribution

The paper proposes MF-TWDPCCA, combining existing methods to effectively remove external influences and quantify true cross-correlations in non-stationary data.

Findings

MF-TWDPCCA accurately detects intrinsic cross-correlations in simulated data.

Application to stock market data reveals significant multifractal cross-correlations.

A new coefficient quantifies the level of intrinsic cross-correlation.

Abstract

When common factors strongly influence two cross-correlated time series recorded in complex natural and social systems, the results will be biased if we use multifractal detrended cross-correlation analysis (MF-DXA) without considering these common factors. Based on multifractal temporally weighted detrended cross-correlation analysis (MF-TWXDFA) proposed by our group and multifractal partial cross-correlation analysis (MF-DPXA) proposed by Qian et al., we propose a new method---multifractal temporally weighted detrended partial cross-correlation analysis (MF-TWDPCCA) to quantify intrinsic power-law cross-correlation of two non-stationary time series affected by common external factors in this paper. We use MF-TWDPCCA to characterize the intrinsic cross-correlations between the two simultaneously recorded time series by removing the effects of other potential time series. To test the performance of MF-TWDPCCA, we apply it, MF-TWXDFA and MF-DPXA on simulated series. Numerical tests on artificially simulated series demonstrate that MF-TWDPCCA can accurately detect the intrinsic cross-correlations for two simultaneously recorded series. To further show the utility of MF-TWDPCCA, we apply it on time series from stock markets and find that there exists significantly multifractal power-law cross-correlation between stock returns. A new partial cross-correlation coefficient is defined to quantify the level of intrinsic cross-correlation between two time series.