title: Universal relation between skewness and kurtosis in complex dynamics.
abstract: We identify an important correlation between skewness and kurtosis for a broad class of complex dynamic systems and present a specific analysis of earthquake and financial time series. Two regimes of non-Gaussianity can be identified: a parabolic one, which is common in various fields of physics, and a power law one, with exponent 4/3, which at the moment appears to be specific of earthquakes and financial markets. For this property we propose a model and an interpretation in terms of very rare events dominating the statistics independently on the nature of the events considered. The predicted scaling relation between skewness and kurtosis matches very well the experimental pattern of the second regime. Regarding price fluctuations, this situation characterizes a universal stylized fact.
authors.affiliation: Department of Physics, University of Rome Sapienza, Piazzale Aldo Moro 5, 00185 Rome, Italy. matthieu.cristelli@roma1.infn.it
authors.forename: Matthieu
authors.initials: M
authors.lastname: Cristelli
authors.forename: Andrea
authors.initials: A
authors.lastname: Zaccaria
authors.forename: Luciano
authors.initials: L
authors.lastname: Pietronero
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D055866:Earthquakes; D005544:Forecasting; D015233:Models, Statistical