Genuine multifractality in time series is due to temporal correlations

作     者：Kwapień, Jaroslaw Blasiak, Pawel Drozdz, Stanislaw Oświȩcimka, Pawel 

作者机构：Complex Systems Theory Department Institute of Nuclear Physics Polish Academy of Sciences ul. Radzikowskiego 152 Kraków31-342 Poland Institute for Quantum Studies Chapman University OrangeCA92866 United States Faculty of Computer Science and Telecommunications Cracow University of Technology ul. Warszawska 24 Kraków31-155 Poland Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University ul. Lojasiewicza 11 Kraków30-348 Poland 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2022年

核心收录：

主　　题：Time series 

摘      要：Based on the mathematical arguments formulated within the Multifractal Detrended Fluctuation Analysis (MFDFA) approach it is shown that in the uncorrelated time series from the Gaussian basin of attraction the effects resembling multifractality asymptotically disappear for positive moments when the length of time series increases. A hint is given that this applies to the negative moments as well and extends to the Lévy stable regime of fluctuations. The related effects are also illustrated and confirmed by numerical simulations. This documents that the genuine multifractality in time series may only result from the long-range temporal correlations and the fatter distribution tails of fluctuations may broaden the width of singularity spectrum only when such correlations are present. The frequently asked question of what makes multifractality in time series - temporal correlations or broad distribution tails - is thus ill posed. In the absence of correlations only the bifractal or monofractal cases are possible. The former corresponds to the Lévy stable regime of fluctuations while the latter to the ones belonging to the Gaussian basin of attraction in the sense of the Central Limit Theorem. Copyright © 2022, The Authors. All rights reserved.