How Statistically Significant is the DMCA Coefficient?

In this paper, we proposed a statistical test for the Detrending Moving-Average Cross-Correlation Coefficient (rho(DMCA)). With this methodology, it is possible to evaluate the statistical significance of rho(DMCA) for different confidence levels. The test was applied to financial market and climatological data. Findings on this research show that rejection or non-rejection of the null hypothesis of rho(DMCA) depends on the size N of the series and the moving average window length tau evaluated. Our findings also show a behavioral pattern in the critical values of rho(DMCA). Fixing the size of the series (N), as the size of the moving average window length tau increases, the critical values tend to increase.