Comparing Multiscale Estimators of the Degree of Multifractality by Detrended Fluctuation Analysis

Some physiological series, like the cardiovascular signals, show multifractal structures that depend on the temporal scale. Thus, their fractal nature is better assessed by a Detrended Fluctuation Analysis (DFA) approach that provides multifractal coefficients scale by scale. Our aim is to compare two estimators of the degree of scale-by-scale multifractality based on the width of the singularity spectrum or on the statistical dispersion of the DFA coefficients. We synthesized 1000 series of white noise (monofractal and monoscale), of autoregressive noise (monofractal and multiscale) and of Cauchy-distributed noise (multifractal and monoscale) comparing the two estimators at scales between 8 and 228 samples. We found that the two estimators provide similar scale-by-scale profiles of multifractality. However, the statistical-dispersion estimator better distinguishes multifractal from monofractal noises at all the scales, thus appearing more suitable than the singularity-spectrum width to describe the fractal structure of physiological time series.