## Detail publikace

### Kristoufek, L.: Fractal approach towards power-law coherency to measure cross-correlations between time series

Autor: prof. PhDr. Ladislav Krištoufek Ph.D., Články v impaktovaných časopisech 2017 0 Communications in Nonlinear Science and Numerical Simulation 50, pp. 193-200 arXiv PDF power-law coherency, power-law cross-correlations, correlations 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.
Prosinec 2020
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