title: Detrended partial cross-correlation analysis of two nonstationary time series influenced by common external forces.
abstract: When common factors strongly influence two power-law cross-correlated time series recorded in complex natural or social systems, using 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 multiscale 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 U.S. 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 multifractal DCCA method fails.
authors.affiliation: School of Science, East China University of Science and Technology, Shanghai 200237, China.|Research Center for Econophysics, East China University of Science and Technology, Shanghai 200237, China.
authors.forename: Xi-Yuan
authors.initials: XY
authors.lastname: Qian
authors.affiliation: School of Science, East China University of Science and Technology, Shanghai 200237, China.
authors.forename: Ya-Min
authors.initials: YM
authors.lastname: Liu
authors.affiliation: Research Center for Econophysics, East China University of Science and Technology, Shanghai 200237, China.|School of Business, East China University of Science and Technology, Shanghai 200237, China.
authors.forename: Zhi-Qiang
authors.initials: ZQ
authors.lastname: Jiang
authors.affiliation: Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.|Faculty of Civil Engineering, University of Rijeka, 51000 Rijeka, Croatia.|Zagreb School of Economics and Management, 10000 Zagreb, Croatia.|Faculty of Economics, University of Ljubljana, 1000 Ljubljana, Slovenia.
authors.forename: Boris
authors.initials: B
authors.lastname: Podobnik
authors.affiliation: School of Science, East China University of Science and Technology, Shanghai 200237, China.|Research Center for Econophysics, East China University of Science and Technology, Shanghai 200237, China.|School of Business, East China University of Science and Technology, Shanghai 200237, China.
authors.forename: Wei-Xing
authors.initials: WX
authors.lastname: Zhou
authors.affiliation: Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: H Eugene
authors.initials: HE
authors.lastname: Stanley