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

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. In order to better study the time series of such cases, we extend the multifractal temporally weighted detrended cross-correlation analysis (MF-TWXDFA) proposed by our group (Wei et al., 2017) and propose 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. To test the performance of MF-TWDPCCA, we apply it and multifractal partial cross-correlation analysis (MF-DPXA) proposed by Qian et al. (2015) on simulated series. Numerical tests on artificially simulated series demonstrate that MF-TWDPCCA can more accurately detect the intrinsic cross-correlations for two simultaneously recorded series than MF-DPXA and MF-TWXDFA. 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. In addition, a new partial cross-correlation coefficient is defined to quantify the level of intrinsic cross-correlation between two time series.