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