Detrended partial cross-correlation analysis of two nonstationary time series influenced by common external forces

摘要

When common factors strongly influence two power-law cross-correlated timeseries recorded in complex natural or social systems, using classic detrendedcross-correlation analysis (DCCA) without considering these common factors willbias the results. We use detrended partial cross-correlation analysis (DPXA) touncover the intrinsic power-law cross-correlations between two simultaneouslyrecorded time series in the presence of nonstationarity after removing theeffects of other time series acting as common forces. The DPXA method is ageneralization of the detrended cross-correlation analysis that takes intoaccount partial correlation analysis. We demonstrate the method by usingbivariate fractional Brownian motions contaminated with a fractional Brownianmotion. We find that the DPXA is able to recover the analytical cross Hurstindices, and thus the multi-scale DPXA coefficients are a viable alternative tothe conventional cross-correlation coefficient. We demonstrate the advantage ofthe DPXA coefficients over the DCCA coefficients by analyzing contaminatedbivariate fractional Brownian motions. We calculate the DPXA coefficients anduse them to extract the intrinsic cross-correlation between crude oil and goldfutures by taking into consideration the impact of the US dollar index. Wedevelop the multifractal DPXA (MF-DPXA) method in order to generalize the DPXAmethod and investigate multifractal time series. We analyze multifractalbinomial measures masked with strong white noises and find that the MF-DPXAmethod quantifies the hidden multifractal nature while the MF-DCCA methodfails.