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Open AccessArticle

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

1
Department of Mathematical Sciences and Computational Science Program, University of Texas at El Paso, El Paso, TX 79968-0514, USA
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Computational Science Program, University of Texas at El Paso, El Paso, TX 79968-0514, USA
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Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968-0514, USA
4
Comisión Nacional de Energía Atómica, Buenos Aires, Argentina
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 441; https://doi.org/10.3390/math8030441
Received: 31 January 2020 / Revised: 6 March 2020 / Accepted: 10 March 2020 / Published: 18 March 2020
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. View Full-Text
Keywords: Diffusion Entropy Analysis; Hurst R/S analysis; Detrended Fluctuation Analysis; Fractional Brownian Motion; long-range correlations Diffusion Entropy Analysis; Hurst R/S analysis; Detrended Fluctuation Analysis; Fractional Brownian Motion; long-range correlations
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Mariani, M.C.; Asante, P.K.; Bhuiyan, M.A.M.; Beccar-Varela, M.P.; Jaroszewicz, S.; Tweneboah, O.K. Long-Range Correlations and Characterization of Financial and Volcanic Time Series. Mathematics 2020, 8, 441.

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