# Dynamic Hurst Exponent in Time Series

## TL;DR

This paper investigates the use of the Hurst exponent to identify different regimes in financial market time series, revealing self-organized critical behavior during market crashes and proposing it as a critical variable akin to phase transitions in physics.

## Contribution

It introduces the Hurst exponent as a tool to distinguish market regimes and demonstrates its effectiveness in identifying critical points in financial time series.

## Key findings

- Hurst exponent effectively identifies market regimes.
- Critical points separate random walk and power law behaviors.
- Hurst exponent acts as a critical variable in market analysis.

## Abstract

The market efficiency hypothesis has been proposed to explain the behavior of time series of stock markets. The Black-Scholes model (B-S) for example, is based on the assumption that markets are efficient. As a consequence, it is impossible, at least in principle, to "predict" how a market behaves, whatever the circumstances. Recently we have found evidence which shows that it is possible to find self-organized behavior in the prices of assets in financial markets during deep falls of those prices. Through a kurtosis analysis we have identified a critical point that separates time series from stock markets in two different regimes: the mesokurtic segment compatible with a random walk regime and the leptokurtic one that allegedly follows a power law behavior. In this paper we provide some evidence, showing that the Hurst exponent is a good estimator of the regime in which the market is operating. Finally, we propose that the Hurst exponent can be considered as a critical variable in just the same way as magnetization, for example, can be used to distinguish the phase of a magnetic system in physics.