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. 2019 Mar 1;10:115. doi: 10.3389/fphys.2019.00115

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Copyright © 2019 Castiglioni and Faini.

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

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F_q(n) functions for a multifractal binomial cascade embedded in noise of N = 65,536 samples. Estimates without overlapping by the traditional (Left) and fast (Center) algorithm and with maximum overlapping by the fast algorithm (Right) were performed over 38 block sizes, with thresholds as in Equations (19) and EPS = 0. On a laptop computer, the traditional algorithm employed T = 4.3 s for DFA₁ and T = 9.5 s for DFA₂ without overlapping while the fast algorithm employed 0.12 s without overlapping and 3.6 s with maximum overlapping for calculating DFA₁ and DFA₂ estimates simultaneously.