  We study finite sample properties of estimators of power-law
cross-correlations -- detrended cross-correlation analysis (DCCA), height
cross-correlation analysis (HXA) and detrending moving-average
cross-correlation analysis (DMCA) -- with a special focus on short-term memory
bias as well as power-law coherency. Presented broad Monte Carlo simulation
study focuses on different time series lengths, specific methods' parameter
setting, and memory strength. We find that each method is best suited for
different time series dynamics so that there is no clear winner between the
three. The method selection should be then made based on observed dynamic
properties of the analyzed series.
