Figure 2.

F_q(n) functions by the traditional (MF DFA) and the proposed fast algorithm (Fast MF DFA) for the {wb_i} series. The series of N = 200,000 samples is the superposition of white noise and Brownian motion (see text); estimates without overlapping by the traditional algorithm (Left) and by our fast algorithm (Center) and with maximum overlapping by our fast algorithm (Right) were performed over 56 block sizes exponentially distributed over the n axis, with thresholds Th₁ and Th₂ as in Equations (19) and EPS = 0. On a laptop computer, the traditional algorithm employed T = 57 s for calculating DFA₁ and T = 146 s for calculating DFA₂ without overlapping, the fast algorithm employed 2.2 s without overlapping and 65 s with maximum overlapping for calculating both the DFA₁ and DFA₂ estimates simultaneously.