Date: September 25, 2002
Creator: Scafetta, Nicola & Grigolini, Paolo
Description: This article discusses scaling detection in time series. The methods currently used to determine the scaling exponent of a complex dynamic process described by a time series are based on the numerical evaluation of variance. This means that all of them can be safely applied only to the case where ordinary statistical properties hold true even if strange kinetics are involved. The authors illustrate a method of statistical analysis based on the Shannon entropy of the diffusion process generated by the time series, called diffusion entropy analysis (DEA). The authors adopt artificial Gauss and Lévy time series, as prototypes of ordinary and anomalous statistics, respectively, and the authors analyze them with the DEA and four ordinary methods of analysis, some of which are very popular. The authors show that the DEA determines the correct scaling exponent even when the statistical properties, as well as the dynamic properties, are anomalous. The other four methods produce correct results in the Gauss case but fail to detect the correct scaling in the case of Lévy statistics.
Contributing Partner: UNT College of Arts and Sciences