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From solar flare time series to fractional dynamics

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  • Burnecki, Krzysztof
  • Klafter, Joseph
  • Magdziarz, Marcin
  • Weron, Aleksander

Abstract

We demonstrate that continuous-time FARIMA processes with α-stable noise provide a new stochastic tool for studying the solar flare phenomenon in the framework of fractional Langevin equation. Simple computer tests to check the origins of α-stability and self-similarity are implemented for empirical time series describing the energy of solar flares. Based on observed physical time series we solve the challenging problem of how to detect long-range dependence from real data and how to model it via fractional dynamics (Langevin or Fokker–Planck). We employ here codifference as a proper measure for long-range dependence. It is applicable to empirical data from the distribution lacking the second moment.

Suggested Citation

  • Burnecki, Krzysztof & Klafter, Joseph & Magdziarz, Marcin & Weron, Aleksander, 2008. "From solar flare time series to fractional dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1077-1087.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:5:p:1077-1087
    DOI: 10.1016/j.physa.2007.10.024
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    References listed on IDEAS

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    1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook9401, December.
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    Cited by:

    1. Rafał Weron, 2009. "Heavy-tails and regime-switching in electricity prices," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 457-473, July.
    2. Graves, Timothy & Franzke, Christian L.E. & Watkins, Nicholas W. & Gramacy, Robert B. & Tindale, Elizabeth, 2017. "Systematic inference of the long-range dependence and heavy-tail distribution parameters of ARFIMA models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 60-71.

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