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Long-Range Correlations and Characterization of Financial and Volcanic Time Series

Author

Listed:
  • Maria C. Mariani

    (Department of Mathematical Sciences and Computational Science Program, University of Texas at El Paso, El Paso, TX 79968-0514, USA)

  • Peter K. Asante

    (Computational Science Program, University of Texas at El Paso, El Paso, TX 79968-0514, USA)

  • Md Al Masum Bhuiyan

    (Computational Science Program, University of Texas at El Paso, El Paso, TX 79968-0514, USA)

  • Maria P. Beccar-Varela

    (Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968-0514, USA)

  • Sebastian Jaroszewicz

    (Comisión Nacional de Energía Atómica, Buenos Aires, Argentina)

  • Osei K. Tweneboah

    (Computational Science Program, University of Texas at El Paso, El Paso, TX 79968-0514, USA)

Abstract

In this study, we use the Diffusion Entropy Analysis (DEA) to analyze and detect the scaling properties of time series from both emerging and well established markets as well as volcanic eruptions recorded by a seismic station, both financial and volcanic time series data have high frequencies. The objective is to determine whether they follow a Gaussian or Lévy distribution, as well as establish the existence of long-range correlations in these time series. The results obtained from the DEA technique are compared with the Hurst R/S analysis and Detrended Fluctuation Analysis (DFA) methodologies. We conclude that these methodologies are effective in classifying the high frequency financial indices and volcanic eruption data—the financial time series can be characterized by a Lévy walk while the volcanic time series is characterized by a Lévy flight.

Suggested Citation

  • Maria C. Mariani & Peter K. Asante & Md Al Masum Bhuiyan & Maria P. Beccar-Varela & Sebastian Jaroszewicz & Osei K. Tweneboah, 2020. "Long-Range Correlations and Characterization of Financial and Volcanic Time Series," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:441-:d:333707
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    References listed on IDEAS

    as
    1. Mariani, M.C. & Liu, Y., 2007. "Normalized truncated Levy walks applied to the study of financial indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(2), pages 590-598.
    2. Christopher Brooks, 1995. "A measure of persistence in daily pound exchange rates," Applied Economics Letters, Taylor & Francis Journals, vol. 2(11), pages 428-431.
    3. Mariani, Maria C. & Bhuiyan, Md Al Masum & Tweneboah, Osei K. & Gonzalez-Huizar, Hector & Florescu, Ionut, 2018. "Volatility models applied to geophysics and high frequency financial market data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 304-321.
    4. E. Barany & M. P. Beccar Varela & I. Florescu & I. Sengupta, 2012. "Detecting market crashes by analysing long-memory effects using high-frequency data," Quantitative Finance, Taylor & Francis Journals, vol. 12(4), pages 623-634, April.
    5. Mariani, Maria C. & Tweneboah, Osei K., 2016. "Stochastic differential equations applied to the study of geophysical and financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 170-178.
    6. Huang, Jingjing & Shang, Pengjian & Zhao, Xiaojun, 2012. "Multifractal diffusion entropy analysis on stock volatility in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5739-5745.
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