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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]

Based on the traditional detrended moving average cross-correlation analysis (DMCA) method and the detrended multiple cross-correlation analysis (DMC) method, we propose the detrended multiple moving average cross-correlation analysis method (DMMC) to quantify the correlation between non-stationary signals on different time scales. It will be the generalization of the correlation between pairwise time series and can be used to measure the multivariate correlation between the dependent variable y with the others i independent variable x. To validate the DMMC method, we determined the DMMC coefficient into numerical simulations on the standard Gaussian distribution, Lognormal distribution t distribution and ARFIMA long memory random sequences. Then we apply the proposed method to explore the multiple correlations between China's Shanghai, Shenzhen, and Hong Kong stock markets and analyze the dynamic time-varying characteristics of the correlation with the sliding window approach. The results show that DMMC is suitable to measure multiple cross-correlations. This new method can be further applied to multiple cross-correlation in different areas of knowledge, such as energy, meteorology, medicine, transportation, etc. • We proposed a new detrended multiple moving average cross-correlation coefficient. • We performed numerical simulations under different distributions. • The results are presented in a new map of colors. [ABSTRACT FROM AUTHOR]