Statistical properties of the detrended multiple cross-correlation coefficient

Cross-correlations are ubiquitous in nonstationary multivariable systems. By using de-trended cross-correlation (DCCA) technique, recently a new multiple cross-correlation coefficient DMC was proposed to quantity the correlation between multivariate and a target variable. We studied the statistical properties of DMC in detail. More specifically, we first proved that 0 <= DMC <= 1, and then deduced that the DMC is approximately chi(2) distributed for overlapping windows with different window size. In addition, the range of DMC 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 DMC. 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 PM2.5 dominates in Beijing's AQI system. (C) 2021 Elsevier B.V. All rights reserved.