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

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 factors. Based on temporally weighted (MF-TWXDFA) proposed by our group partial (MF-DPXA) Qian et al., propose a new method---multifractal (MF-TWDPCCA) to quantify intrinsic power-law of non-stationary affected external this paper. We MF-TWDPCCA characterize cross-correlations between simultaneously removing effects other potential series. To test performance MF-TWDPCCA, apply it, MF-TWXDFA MF-DPXA simulated Numerical tests artificially demonstrate that can accurately detect for further show utility it from stock markets find there exists significantly returns. A coefficient is defined level