  Notwithstanding the significant efforts to develop estimators of long-range
correlations (LRC) and to compare their performance, no clear consensus exists
on what is the best method and under which conditions. In addition, synthetic
tests suggest that the performance of LRC estimators varies when using
different generators of LRC time series. Here, we compare the performances of
four estimators [Fluctuation Analysis (FA), Detrended Fluctuation Analysis
(DFA), Backward Detrending Moving Average (BDMA), and centred Detrending Moving
Average (CDMA)]. We use three different generators [Fractional Gaussian Noises,
and two ways of generating Fractional Brownian Motions]. We find that CDMA has
the best performance and DFA is only slightly worse in some situations, while
FA performs the worst. In addition, CDMA and DFA are less sensitive to the
scaling range than FA. Hence, CDMA and DFA remain "The Methods of Choice" in
determining the Hurst index of time series.
