Quantifying cross-correlations using local and global detrendingapproaches

摘要

In order to quantify the long-range cross-correlations between two time series qualitatively, weintroduce a new cross-correlations test QCC (m), where m is the number of degrees of freedom. If thereare no cross-correlations between two time series, the cross-correlation test agrees well with the x2(m)distribution. If the cross-correlations test exceeds the critical value of the x2 (m) distribution, then we saythat the cross-correlations are significant. We show that if a Fourier phase-randofnization procedure iscarried out on a power-law cross-correlated time series, the cross-correlations test is substantially reducedcompared to the case before Fourier phase randomization. We also study the effect of periodic trends onsystems with power-law cross-correlations. We find that periodic trends can severely affect the quantitativeanalysis of long-range correlations, leading to crossovers and other spurious deviations from power laws,implying both local and global detrending approaches should be applied to properly uncover long-rangepower-law auto-correlations and cross-correlations in the random part of the underlying stochastic process.