  We examine several recently suggested methods for the detection of long-range
correlations in data series based on similar ideas as the well-established
Detrended Fluctuation Analysis (DFA). In particular, we present a detailed
comparison between the regular DFA and two recently suggested methods: the
Centered Moving Average (CMA) Method and a Modified Detrended Fluctuation
Analysis (MDFA). We find that CMA is performing equivalently as DFA in long
data with weak trends and slightly superior to DFA in short data with weak
trends. When comparing standard DFA to MDFA we observe that DFA performs
slightly better in almost all examples we studied. We also discuss how several
types of trends affect the different types of DFA. For weak trends in the data,
the new methods are comparable with DFA in these respects. However, if the
functional form of the trend in data is not a-priori known, DFA remains the
method of choice. Only a comparison of DFA results, using different detrending
polynomials, yields full recognition of the trends. A comparison with
independent methods is recommended for proving long-range correlations.
