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 with the others independent variable . To validate the DMMC method, we determined the DMMC coefficient into numerical simulations on the standard Gaussian distribution, Lognormal distribution 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.
Detrended multiple moving average cross-correlation analysis and its application in the correlation measurement of stock market in Shanghai, Shenzhen, and Hong Kong☆