SEVERAL FUNDAMENTAL PROPERTIES OF DCCA CROSS-CORRELATION COEFFICIENT

Abstract

The (detrended cross-correlation analysis) DCCA cross-correlation coefficient was proposed to measure the level of long-range cross-correlations between two non-stationary time series on multiple time scales. It has been applied to diverse areas of interest, although many properties of this method are not clear. In this paper, we theoretically study several fundamental properties of the DCCA cross-correlation coefficient, which contributes to acquiring more statistical characteristics of this measure. We resort to a synthetic time series that is followed by the integration and the detrending procedures of the DCCA cross-correlation coefficient, which divide the steps to estimate the coefficient into two portions. The former portion, including the integration and the detrending, is proved to be a linear transformation. The second portion is devoted to measuring Pearson’s [Formula: see text] between two synthetic time series. We confirm that the DCCA cross-correlation coefficient is also a linear measure by definition. The simulations including the ARFIMA processes and the multifractal binomial measures are numerically analyzed, which confirm the theoretical analysis.