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Dynamic Hurst Exponent in Time Series

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  • Carlos Arturo Soto Campos
  • Leopoldo S'anchez Cant'u
  • Zeus Hern'andez Veleros

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.

Suggested Citation

  • Carlos Arturo Soto Campos & Leopoldo S'anchez Cant'u & Zeus Hern'andez Veleros, 2019. "Dynamic Hurst Exponent in Time Series," Papers 1903.07809, arXiv.org.
    • Handle: RePEc:arx:papers:1903.07809
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    References listed on IDEAS

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    1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Nevi Danila, 2022. "Random Walk of Socially Responsible Investment in Emerging Market," Sustainability, MDPI, vol. 14(19), pages 1-13, September.

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