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

Abstract

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 ${\rho }_{DMCA}(\lambda )$ with a moving average window length $\lambda$. 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 ${\rho }_{DMCA}(\lambda )$ 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.

8 pages, 4 figures

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