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Scaling properties and entropy of long-range correlated time series

Author

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  • Carbone, Anna
  • Stanley, H. Eugene

Abstract

We calculate the Shannon entropy of a time series by using the probability density functions of the characteristic sizes of the long-range correlated clusters introduced in [A. Carbone, G. Castelli, H.E. Stanley, Phys. Rev. E 69 (2004) 026105]. We define three different measures of the entropy related, respectively, to the length, the duration and the area of the clusters. For all the three cases, the entropy increases as the logarithm of a power of the size with exponents equal to the fractal dimension of the cluster length, duration and area, respectively.

Suggested Citation

  • Carbone, Anna & Stanley, H. Eugene, 2007. "Scaling properties and entropy of long-range correlated time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(1), pages 21-24.
    • Handle: RePEc:eee:phsmap:v:384:y:2007:i:1:p:21-24
    DOI: 10.1016/j.physa.2007.04.105
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    Citations

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    Cited by:

    1. Zunino, Luciano & Tabak, Benjamin M. & Serinaldi, Francesco & Zanin, Massimiliano & Pérez, Darío G. & Rosso, Osvaldo A., 2011. "Commodity predictability analysis with a permutation information theory approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(5), pages 876-890.
    2. Wesfreid, Eva & Billat, Véronique, 2012. "Randomness and changes of heart rate and respiratory frequency during high altitude mountain ascent without acclimatization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1575-1590.
    3. Dumansky, Y.V. & Lyakh, Y.E. & Gorshkov, O.G. & Gurianov, V.G. & Prihodchenko, V.V., 2012. "Fractal dimensionality analysis of normal and cancerous mammary gland thermograms," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1494-1500.
    4. Ponta, Linda & Carbone, Anna, 2018. "Information measure for financial time series: Quantifying short-term market heterogeneity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 132-144.
    5. Pietro Murialdo & Linda Ponta & Anna Carbone, 2020. "Long-Range Dependence in Financial Markets: a Moving Average Cluster Entropy Approach," Papers 2004.14736, arXiv.org.
    6. Gajda, Janusz & Bartnicki, Grzegorz & Burnecki, Krzysztof, 2018. "Modeling of water usage by means of ARFIMA–GARCH processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 644-657.
    7. Chapeau-Blondeau, François & Rousseau, David, 2009. "The minimum description length principle for probability density estimation by regular histograms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(18), pages 3969-3984.
    8. Potirakis, S.M. & Minadakis, G. & Eftaxias, K., 2012. "Analysis of electromagnetic pre-seismic emissions using Fisher information and Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 300-306.
    9. Kalimeri, M. & Papadimitriou, C. & Balasis, G. & Eftaxias, K., 2008. "Dynamical complexity detection in pre-seismic emissions using nonadditive Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1161-1172.
    10. 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.
    11. Stanley, H. Eugene & Plerou, Vasiliki & Gabaix, Xavier, 2008. "A statistical physics view of financial fluctuations: Evidence for scaling and universality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3967-3981.
    12. Ponta, Linda & Murialdo, Pietro & Carbone, Anna, 2021. "Information measure for long-range correlated time series: Quantifying horizon dependence in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).
    13. Farzadian, O. & Niry, M.D., 2016. "Delocalization of mechanical waves in the ladder chain of DNA with correlated disorder," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 95-103.

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