Inter-occurrence times and universal laws in finance, earthquakes and genomes

TL;DR

This paper explores universal statistical laws governing inter-occurrence times across diverse systems like finance, earthquakes, and genomes, highlighting the role of nonadditive $q$-statistics in describing their behaviors.

Contribution

It demonstrates that inter-occurrence times in various complex systems follow universal patterns describable by $q$-statistics, revealing common underlying principles.

Findings

Inter-occurrence times exhibit universal distribution patterns.

$q$-statistics effectively models diverse complex systems.

Universal laws connect finance, earthquakes, and genomes.

Abstract

A plethora of natural, artificial and social systems exist which do not belong to the Boltzmann-Gibbs (BG) statistical-mechanical world, based on the standard additive entropy $S_{BG}$ and its associated exponential BG factor. Frequent behaviors in such complex systems have been shown to be closely related to $q$-statistics instead, based on the nonadditive entropy $S_q$ (with $S_1=S_{BG}$), and its associated $q$-exponential factor which generalizes the usual BG one. In fact, a wide range of phenomena of quite different nature exist which can be described and, in the simplest cases, understood through analytic (and explicit) functions and probability distributions which exhibit some universal features. Universality classes are concomitantly observed which can be characterized through indices such as $q$. We will exhibit here some such cases, namely concerning the distribution of inter-occurrence (or inter-event) times in the areas of finance, earthquakes and genomes.