Figure 1

The scaling function $\tau (q)$ for the multifractal process with log-normally distributed multiplicators. (a),(c) Means (full circles) and 95% of distributions (vertical bars) of 1000 realizations of the process. (b),(d) $\tau (q)$ values (full circles) for a particular realization of the multifractal process; and 95% of distribution (vertical bars) of 1000 realizations of the multifractal surrogate data constructed from the one process realization. The used time series length was 65536 (a),(b) and 4096 (c),(d) samples. The solid line shows theoretical values according to the analytic formula.Reuse & Permissions

Figure 2

The scaling function $\tau (q)$ for a particular realization of the multifractal process (full circles) and 95% of distribution (vertical bars) of 1000 realizations of (a) IAFT, (b) permutated wavelet coefficients, (c) cyclically rotated wavelet coefficients, and (d) multifractal surrogate data. The surrogate means are connected by the thin solid lines, the thick solid lines show the theoretical $\tau (q)$.Reuse & Permissions

Figure 3

Autocorrelation function of a realization of the multifractal process (full circles) and 95% of distribution (vertical bars) of 1000 realizations of (a) IAFT, (b) permutated wavelet coefficients, (c) cyclically rotated wavelet coefficients, and (d) multifractal surrogate data.Reuse & Permissions

Figure 4

(Auto) mutual information function of a realization of the multifractal process (full circles) and 95% of distribution (vertical bars) of 1000 realizations of (a) IAFT, (b) permutated wavelet coefficients, (c) cyclically rotated wavelet coefficients, and (d) multifractal surrogate data.Reuse & Permissions