Dynamical analogy between economical crisis and earthquake dynamics within the nonextensive statistical mechanics framework

Abstract

The field of study of complex systems considers that the dynamics of complex systems are founded on universal principles that may be used to describe a great variety of scientific and technological approaches of different types of natural, artificial, and social systems. Several authors have suggested that earthquake dynamics and the dynamics of economic (financial) systems can be analyzed within similar mathematical frameworks. We apply concepts of the nonextensive statistical physics, on time-series data of observable manifestations of the underlying complex processes ending up with these different extreme events, in order to support the suggestion that a dynamical analogy exists between a financial crisis (in the form of share or index price collapse) and a single earthquake. We also investigate the existence of such an analogy by means of scale-free statistics (the Gutenberg–Richter distribution of event sizes). We show that the populations of: (i) fracto-electromagnetic events rooted in the activation of a single fault, emerging prior to a significant earthquake, (ii) the trade volume events of different shares/economic indices, prior to a collapse, and (iii) the price fluctuation (considered as the difference of maximum minus minimum price within a day) events of different shares/economic indices, prior to a collapse, follow both the traditional Gutenberg–Richter law as well as a nonextensive model for earthquake dynamics, with similar parameter values. The obtained results imply the existence of a dynamic analogy between earthquakes and economic crises, which moreover follow the dynamics of seizures, magnetic storms and solar flares.