Statistical test for Detrended Multiple Cross-Correlation Coefficient

Abstract Cross-correlations are ubiquitous in nonstationary multivariable systems. By using detrended cross-correlation (DCCA) technique, recently a new multiple cross-correlation coefficient D M C was proposed to quantity the correlation between multivariate and a target variable. We studied the statistical properties of D M C in detail. More specifically, we first proved that 0 ≤ D M C ≤ 1 , and then deduced that the D M C is approximately χ 2 distributed for overlapping windows with different window size. In addition, the range of D M C was determined numerically by statistical test, where the multiple correlations can be regarded as statistically significant. Furthermore, we discussed the influence of the cross-correlation among the target variable and independent variables on D M C . Finally, by utilizing this statistical test on financial system and environment data, we found that the US dollar index affects international gold spot prices and West Texas Intermediate oil price greatly, and PM 2.5 dominates in Beijing’s AQI system.