title: Log-amplitude statistics for Beck-Cohen superstatistics.
abstract: As a possible generalization of Beck-Cohen superstatistical processes, we study non-Gaussian processes with temporal heterogeneity of local variance. To characterize the variance heterogeneity, we define log-amplitude cumulants and log-amplitude autocovariance and derive closed-form expressions of the log-amplitude cumulants for χ(2), inverse χ(2), and log-normal superstatistical distributions. Furthermore, we show that χ(2) and inverse χ(2) superstatistics with degree 2 are closely related to an extreme value distribution, called the Gumbel distribution. In these cases, the corresponding superstatistical distributions result in the q-Gaussian distribution with q=5/3 and the bilateral exponential distribution, respectively. Thus, our finding provides a hypothesis that the asymptotic appearance of these two special distributions may be explained by a link with the asymptotic limit distributions involving extreme values. In addition, as an application of our approach, we demonstrated that non-Gaussian fluctuations observed in a stock index futures market can be well approximated by the χ(2) superstatistical distribution with degree 2.
authors.affiliation: Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan.
authors.forename: Ken
authors.initials: K
authors.lastname: Kiyono
authors.forename: Hidetoshi
authors.initials: H
authors.lastname: Konno
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D015233:Models, Statistical