Estimation of multifractality based on natural time analysis

Recent studies have shown that results deduced on the basis of a new time domain termed natural time reveal that novel dynamical features hidden behind time-series in complex systems can be uncovered. Here, we propose a method for estimating the multifractal behavior of time series by studying the fluctuations of natural time under time reversal. Examples of the application of this method to fractional Gaussian noises, fractional Brownian motions, binomial multifractal series, Lévy processes as well as interbeat intervals' time series from electrocardiograms are presented.