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 to 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) fractoelectromagnetic 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.

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“…In the case of noisy time series, the value of q is often selected such that the signal is better discriminated from the noise and this value of the entropic index is considered to be related to the (multi)fractal structure of the signal(s) under study, which in turn reflects the deep microscopic or mesoscopic (generically non-linear) dynamics in the phase space of the underlying system (Tsallis, 1998). However, if possible, the appropriate value of q should be selected by other independent means, like the best fit to models or distributions expressing the dynamics of the underlying system (Tsallis and de Albuquerque, 2000;Minadakis et al, 2012a,b;Potirakis et al, 2013;Vallianatos, 2013;Efstathiou et al, 2016;Michas et al, 2016).…”

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“…The relatively new field of complex systems increasingly gains the interest of scientists working on disciplines ranging from physics and engineering to economics, biosciences, and social sciences, e.g., [1][2][3][4][5][6][7][8]. The unique characteristic of complex systems is that they may have certain quantitative features that are intriguingly similar, while their dynamics are governed by a set of universal principles [9,10]. Thus, complex systems from different disciplines are often analyzed within similar mathematical frameworks.…”

“…A number of analysis methods have been mutually used to study the dynamics of financial markets, earthquakes, and magnetosphere, e.g., [17,[32][33][34][35][38][39][40][41][42][43][44][45][46][47][48][49][50]. Several authors have suggested that earthquake dynamics and the dynamics of economic (financial) systems can be analyzed within similar mathematical frameworks, e.g., [10] and references therein [14,[51][52][53][54]. On the other hand, authors have also suggested that earthquake dynamics and MSs dynamics can be analyzed within similar mathematical frameworks, as well, e.g., [33][34][35].…”