A criterion for the determination of optimal scaling ranges in DFA and MF-DFA

• We develop a criterion to determine optimal fitting regions in DFA and MF-DFA.
• We use it on several artificial series and find good agreement with known parameters.
• We show that crossover scales can be objectively estimated with this method.
• We also examine monthly sunspot data and confirm previous scaling results.

We develop a criterion based on a brute-force algorithm to systematically determine optimal fitting regions for fluctuation functions in Detrended Fluctuation Analysis (DFA) and Multifractal Detrended Fluctuation Analysis (MF-DFA). We analyze and compare results with several artificially generated time series with known parameters as illustrative examples of this technique. We show that crossover time scales can also be objectively and efficiently estimated using the introduced algorithm. Finally, we employ the proposed methodology to study the scaling behavior of a natural time series: monthly sunspot data previously filtered with empirical mode decomposition (EMD); in this case we find results comparable with those found in the literature.