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We focus on power-law coherency as an alternative approach towards studyingpower-law cross-correlations between simultaneously recorded time series. To beable to study empirical data, we introduce three estimators of the power-lawcoherency parameter $H_{\rho}$ based on popular techniques usually utilized forstudying power-law cross-correlations -- detrended cross-correlation analysis(DCCA), detrending moving-average cross-correlation analysis (DMCA) and heightcross-correlation analysis (HXA). In the finite sample properties study, wefocus on the bias, variance and mean squared error of the estimators. We findthat the DMCA-based method is the safest choice among the three. The HXA methodis reasonable for long time series with at least $10^4$ observations, which canbe easily attainable in some disciplines but problematic in others. TheDCCA-based method does not provide favorable properties which even deterioratewith an increasing time series length. The paper opens a new venue towardsstudying cross-correlations between time series.

Fractal approach towards power-law coherency to measure cross-correlations between time series