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In this paper, we first proposed a statistical test for the detrended multiple moving average cross-correlation coefficient DMMC (s). The DMMC (s) mainly was used to analyze the correlation between the dependent variable y and other n independent variables x i . We proved that DMMC (s) approximately obeys the chi-square distribution. We studied the statistical properties of the DMMC (s) between normally distributed random sequences and power-law ARFIMA long memory random sequences. Furthermore, we discussed the influence of the cross-correlation among the target variable and independent variables on DMMC (s). Finally, we further study the application of DMMC (s) to China's stock markets and China carbon emission trading markets to investigate multiple cross-correlation. The empirical results show that there is a strong multiple correlation between China's Shanghai, Shenzhen and Hong Kong stock markets, while the correlation between China's carbon markets is not significant. This paper provides new ideas and theoretical support for exploring the correlation between multiple variables, which has implications for investors and policymakers. [ABSTRACT FROM AUTHOR]