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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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