  Detrended Fluctuation Analysis (DFA) is the most popular fractal analytical
technique used to evaluate the strength of long-range correlations in empirical
time series in terms of the Hurst exponent, $H$. Specifically, DFA quantifies
the linear regression slope in log-log coordinates representing the
relationship between the time series' variability and the number of timescales
over which this variability is computed. We compared the performance of two
methods of fractal analysis -- the current gold standard, DFA, and a Bayesian
method that is not currently well-known in behavioral sciences: the
Hurst-Kolmogorov (HK) method -- in estimating the Hurst exponent of synthetic
and empirical time series. Simulations demonstrate that the HK method
consistently outperforms DFA in three important ways. The HK method: (i)
accurately assesses long-range correlations when the measurement time series is
short, (ii) shows minimal dispersion about the central tendency, and (iii)
yields a point estimate that does not depend on the length of the measurement
time series or its underlying Hurst exponent. Comparing the two methods using
empirical time series from multiple settings further supports these findings.
We conclude that applying DFA to synthetic time series and empirical time
series during brief trials is unreliable and encourage the systematic
application of the HK method to assess the Hurst exponent of empirical time
series in behavioral sciences.
