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The Effect of the Underlying Distribution in Hurst Exponent Estimation

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  • Miguel Ángel Sánchez
  • Juan E Trinidad
  • José García
  • Manuel Fernández

Abstract

In this paper, a heavy-tailed distribution approach is considered in order to explore the behavior of actual financial time series. We show that this kind of distribution allows to properly fit the empirical distribution of the stocks from S&P500 index. In addition to that, we explain in detail why the underlying distribution of the random process under study should be taken into account before using its self-similarity exponent as a reliable tool to state whether that financial series displays long-range dependence or not. Finally, we show that, under this model, no stocks from S&P500 index show persistent memory, whereas some of them do present anti-persistent memory and most of them present no memory at all.

Suggested Citation

  • Miguel Ángel Sánchez & Juan E Trinidad & José García & Manuel Fernández, 2015. "The Effect of the Underlying Distribution in Hurst Exponent Estimation," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-17, May.
    • Handle: RePEc:plo:pone00:0127824
    DOI: 10.1371/journal.pone.0127824
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    Cited by:

    1. Ramos-Requena, J.P. & Trinidad-Segovia, J.E. & Sánchez-Granero, M.A., 2017. "Introducing Hurst exponent in pair trading," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 488(C), pages 39-45.
    2. José Pedro Ramos-Requena & Juan Evangelista Trinidad-Segovia & Miguel Ángel Sánchez-Granero, 2020. "An Alternative Approach to Measure Co-Movement between Two Time Series," Mathematics, MDPI, vol. 8(2), pages 1-24, February.
    3. Sánchez-Granero, M.A. & Balladares, K.A. & Ramos-Requena, J.P. & Trinidad-Segovia, J.E., 2020. "Testing the efficient market hypothesis in Latin American stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    4. López-García, M.N. & Trinidad-Segovia, J.E. & Sánchez-Granero, M.A. & Pouchkarev, I., 2021. "Extending the Fama and French model with a long term memory factor," European Journal of Operational Research, Elsevier, vol. 291(2), pages 421-426.
    5. V Dimitrova & M Fernández-Martínez & M A Sánchez-Granero & J E Trinidad Segovia, 2019. "Some comments on Bitcoin market (in)efficiency," PLOS ONE, Public Library of Science, vol. 14(7), pages 1-14, July.
    6. A. Gómez-Águila & J. E. Trinidad-Segovia & M. A. Sánchez-Granero, 2022. "Improvement in Hurst exponent estimation and its application to financial markets," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-21, December.
    7. José Pedro Ramos-Requena & Juan Evangelista Trinidad-Segovia & Miguel Ángel Sánchez-Granero, 2020. "Some Notes on the Formation of a Pair in Pairs Trading," Mathematics, MDPI, vol. 8(3), pages 1-17, March.

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