Detrended Multiple Cross-Correlation Coefficient

Based on the detrended cross-correlation coefficient, ρxa,xb, we propose in this paper to establish a Detrended Multiple Cross-Correlation coefficient, DMCx2, to be applied in order to quantify the relations between non-stationary signals on different time scales. This Detrended Multiple Cross-Correlation coefficient will be the measure of the total association between the dependent variable, y, with the others i independent variables, x. It will be the generalization of ρxa,xb, for more than two independent variables. To validate DMCx2, we set up a cross-correlation table (ranging from 0 to 1), and we determined the Detrended Multiple Cross-Correlation coefficient into simulated and real time series. The results of this analysis show that the Detrended Multiple Cross-Correlation coefficient may be suitable and useful to measure multiple cross-correlations, as we will see in this paper.