Figure 2. An illustration of the importance in studying temporal evolution of correlation.
Three artificial time series are generated according to equation (1). (a,c) are the DCCA results for pair {x1, x2} and pair {x1, x3}, respectively. As expected, for pair {x1, x2}, significant correlations are found on time scale of 100, while for pair {x1, x3}, no correlations are found over all time scales. (b,d) show the temporal evolution of the correlation on time scale of 100, for pair {x1, x2} and pair {x1, x3}, respectively. One can see the reason why no correlations are found in (c) is, that there are opposite correlations over time for the pair {x1, x3} on time scale of 100.