# Evidence for criticality in financial data

## TL;DR

This paper presents evidence of critical behavior in financial data, showing that the distribution of absolute normalized returns follows a q-Gaussian form with parameters indicating a phase transition-like phenomenon across different time scales.

## Contribution

It demonstrates that financial returns exhibit criticality modeled by q-Gaussians, linking nonextensive statistical mechanics to financial market behavior.

## Key findings

- Distribution fits q-Gaussian form across time scales
- Parameters q and β are monotonically related
- Critical exponents are numerically determined

## 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.