Detrending moving-average cross-correlation coefficient: Measuring cross-correlations between non-stationary series

In the paper, we introduce a new measure of correlation between possibly non-stationary series. As the measure is based on the detrending moving-average cross-correlation analysis (DMCA), we label it as the DMCA coefficient ρDMCA(λ) with a moving average window length λ. We analytically show that the coefficient ranges between −1 and 1 as a standard correlation does. In the simulation study, we show that the values of ρDMCA(λ) very well correspond to the true correlation between the analyzed series regardless the (non-)stationarity level. Dependence of the newly proposed measure on other parameters–correlation level, moving average window length and time series length–is discussed as well.