Figure 1.

Effect of blocks overlapping on variability and computation time of F_q(n) estimates. (Upper) DFA₁ fluctuation functions for an autoregressive series {x_i} of N = 16,384 samples generated as x_i = ax_i−1+wn_i where wn_i is white Gaussian noise with zero mean and unit variance and a = 0.9391014 as in Kiyono (2015), corresponding to a low-pass filter with cut-off frequency f_co = 0.01, or a cross-over scale n_co = 100 (Höll and Kantz, 2015); calculation time for estimating F_q(n) over 38 block-sizes n was 4 s without overlapping and 3 min with maximum overlapping on a personal computer. (Lower) DFA₁ fluctuation functions for N = 300,000 random samples with Cauchy distribution (location 0, scale 3); calculation time for estimating F_q(n) over 55 block-sizes n was 58 s without overlapping, 5 h and 22 min with maximum overlapping.