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

Maria C. Mariani, Peter K. Asante, Md Al Masum Bhuiyan, Maria P. Beccar-Varela, Sebastian Jaroszewicz and Osei K. Tweneboah
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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

Mathematics, 2020, vol. 8, issue 3, 1-18

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.

Keywords: Diffusion Entropy Analysis; Hurst R/S analysis; Detrended Fluctuation Analysis; Fractional Brownian Motion; long-range correlations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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