Eur. Phys. J. B (2018) 91: 1
https://doi.org/10.1140/epjb/e2017-80535-3

Regular Article

Evidence for criticality in financial data

¹ Departamento de Matemática Aplicada a la Ingeniería Técnica Aeronáutica, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros 3, 28040 Madrid, Spain
² Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, Brazil
³ Escuela Técnica Superior de Ingeniería Aeronáutical y del Espacio, Universidad Politécnica de Madrid, Madrid, Spain

^a e-mail: guiomar.ruiz@upm.es

Received: 21 February 2017
Received in final form: 20 September 2017
Published online: 15 January 2018

Abstract

We provide evidence that cumulative distributions of absolute normalized returns for the 100 American companies with the highest market capitalization, uncover a critical behavior for different time scales Δt. Such cumulative distributions, in accordance with a variety of complex – and financial – systems, can be modeled by the cumulative distribution functions of q-Gaussians, the distribution function that, in the context of nonextensive statistical mechanics, maximizes a non-Boltzmannian entropy. These q-Gaussians are characterized by two parameters, namely (q, β), that are uniquely defined by Δt. From these dependencies, we find a monotonic relationship between q and β, which can be seen as evidence of criticality. We numerically determine the various exponents which characterize this criticality.