Evidence for criticality in financial data

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 $\Delta t$. 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 $(q,\beta)$, that are uniquely defined by $\Delta t$. From these dependencies, we find a monotonic relationship between $q$ and $\beta$, which can be seen as evidence of criticality. We numerically determine the various exponents which characterize this criticality.