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Introducing fractal dimension algorithms to calculate the Hurst exponent of financial time series

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Abstract

In this paper, three new algorithms are introduced in order to explore long memory in financial time series. They are based on a new concept of fractal dimension of a curve. A mathematical support is provided for each algorithm and its accuracy is tested for different length time series by Monte Carlo simulations. In particular, in the case of short length series, the introduced algorithms perform much better than the classical methods. Finally, an empirical application for some stock market indexes as well as some individual stocks is presented.

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Authors and Affiliations

  1. Area of Geometry and Topology, Faculty of Science, Universidad de Almería, 04120, Almería, Spain

    M. J. Sánchez-Granero & M. Fernández-Martínez

  2. Department of Accounting and Finance, Faculty of Economics and Business, Universidad de Almería, 04120, Almería, Spain

    J. E. Trinidad-Segovia

Authors
  1. M. J. Sánchez-Granero
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  2. M. Fernández-Martínez
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  3. J. E. Trinidad-Segovia
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Correspondence to J. E. Trinidad-Segovia.

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Sánchez-Granero, M.J., Fernández-Martínez, M. & Trinidad-Segovia, J.E. Introducing fractal dimension algorithms to calculate the Hurst exponent of financial time series. Eur. Phys. J. B 85, 86 (2012). https://doi.org/10.1140/epjb/e2012-20803-2

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