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Evidence for criticality in financial data

Author

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  • G. Ruiz

    (Departamento de Matemática Aplicada a la Ingeniería Técnica Aeronáutica, Universidad Politécnica de Madrid
    Centro Brasileiro de Pesquisas Fisicas)

  • A. F. de Marcos

    (Escuela Técnica Superior de Ingeniería Aeronáutical y del Espacio, Universidad Politécnica de Madrid)

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.

Suggested Citation

  • G. Ruiz & A. F. de Marcos, 2018. "Evidence for criticality in financial data," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(1), pages 1-5, January.
    • Handle: RePEc:spr:eurphb:v:91:y:2018:i:1:d:10.1140_epjb_e2017-80535-3
    DOI: 10.1140/epjb/e2017-80535-3
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    References listed on IDEAS

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    1. Elvis Oltean, 2016. "Modelling income, wealth, and expenditure data by use of Econophysics," Papers 1603.08383, arXiv.org.
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    Cited by:

    1. Tsallis, Constantino & Borges, Ernesto P., 2021. "Comment on “Pricing of financial derivatives based on the Tsallis statistical theory” by Zhao, Pan, Yue and Zhang," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    2. Arias-Calluari, Karina & Najafi, Morteza. N. & Harré, Michael S. & Tang, Yaoyue & Alonso-Marroquin, Fernando, 2022. "Testing stationarity of the detrended price return in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    3. Trindade, Marco A.S. & Floquet, Sergio & Filho, Lourival M. Silva, 2020. "Portfolio theory, information theory and Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    4. Rovenchak, Andrij & Sobko, Bohdana, 2019. "Fugacity versus chemical potential in nonadditive generalizations of the ideal Fermi-gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).

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    Keywords

    Statistical and Nonlinear Physics;

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