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 $ρ_{DMCA}(λ)$ 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 $ρ_{DMCA}(λ)$ 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.

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