Detecting multifractal stochastic processes under heavy-tailed effects

• Published in: Chaos, solitons and fractals solitons and fractals, 2014-08, Vol.65, p.78-89
• Main Authors: Grahovac, Danijel, Leonenko, Nikolai N.
• Format: Article
• Language: English
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2014.04.016

•Partition function method can be used to detect multifractality of time series.•Nonlinear estimated scaling functions and nontrivial spectrum are characteristic for multifractal processes.•We show that processes with heavy-tailed increments exhibit multifractal features.•Examples are presented, comparing simulated and real data, suspected to be multifractal. Multifractality of a time series can be analyzed using the partition function method based on empirical moments of the process. In this paper we analyze the method when the underlying process has heavy-tailed increments. A nonlinear estimated scaling function and non-trivial spectrum are usually considered as signs of a multifractal property in the data. We show that a large class of processes can produce these effects and that this behavior can be attributed to heavy tails of the process increments. Examples are provided indicating that multifractal features considered can be reproduced by simple heavy-tailed Lévy process.