  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.

Physics and Society;Data Analysis, Statistics and Probability;Statistical Finance