  When common factors strongly influence two power-law cross-correlated time
series recorded in complex natural or social systems, using classic detrended
cross-correlation analysis (DCCA) without considering these common factors will
bias the results. We use detrended partial cross-correlation analysis (DPXA) to
uncover the intrinsic power-law cross-correlations between two simultaneously
recorded time series in the presence of nonstationarity after removing the
effects of other time series acting as common forces. The DPXA method is a
generalization of the detrended cross-correlation analysis that takes into
account partial correlation analysis. We demonstrate the method by using
bivariate fractional Brownian motions contaminated with a fractional Brownian
motion. We find that the DPXA is able to recover the analytical cross Hurst
indices, and thus the multi-scale DPXA coefficients are a viable alternative to
the conventional cross-correlation coefficient. We demonstrate the advantage of
the DPXA coefficients over the DCCA coefficients by analyzing contaminated
bivariate fractional Brownian motions. We calculate the DPXA coefficients and
use them to extract the intrinsic cross-correlation between crude oil and gold
futures by taking into consideration the impact of the US dollar index. We
develop the multifractal DPXA (MF-DPXA) method in order to generalize the DPXA
method and investigate multifractal time series. We analyze multifractal
binomial measures masked with strong white noises and find that the MF-DPXA
method quantifies the hidden multifractal nature while the MF-DCCA method
fails.
