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Evidence for criticality in financial data

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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.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada a la Ingeniería Técnica Aeronáutica, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros 3, 28040, Madrid, Spain

    G. Ruiz

  2. Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud 150, Rio de Janeiro, 22290-180, Brazil

    G. Ruiz

  3. Escuela Técnica Superior de Ingeniería Aeronáutical y del Espacio, Universidad Politécnica de Madrid, Madrid, Spain

    A. F. de Marcos

Authors
  1. G. Ruiz
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  2. A. F. de Marcos
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Correspondence to G. Ruiz.

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Ruiz, G., de Marcos, A.F. Evidence for criticality in financial data. Eur. Phys. J. B 91, 1 (2018). https://doi.org/10.1140/epjb/e2017-80535-3

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  • DOI: https://doi.org/10.1140/epjb/e2017-80535-3

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