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Transitions between superstatistical regimes: Validity, breakdown and applications

Author

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  • Jizba, Petr
  • Korbel, Jan
  • Lavička, Hynek
  • Prokš, Martin
  • Svoboda, Václav
  • Beck, Christian

Abstract

Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important rôle in analysis of hierarchical complex dynamical systems. Yet, its “canonical” formulation in terms of a single nuisance parameter is often too restrictive when applied to complex empirical data. Here we show that a multi-scale generalization of the superstatistics paradigm is more versatile, allowing to address such pertinent issues as transmutation of statistics or inter-scale stochastic behavior. To put some flesh on the bare bones, we provide a numerical evidence for a transition between two superstatistics regimes, by analyzing high-frequency (minute-tick) data for share-price returns of seven selected companies. Salient issues, such as breakdown of superstatistics in fractional diffusion processes or connection with Brownian subordination are also briefly discussed.

Suggested Citation

  • Jizba, Petr & Korbel, Jan & Lavička, Hynek & Prokš, Martin & Svoboda, Václav & Beck, Christian, 2018. "Transitions between superstatistical regimes: Validity, breakdown and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 29-46.
    • Handle: RePEc:eee:phsmap:v:493:y:2018:i:c:p:29-46
    DOI: 10.1016/j.physa.2017.09.109
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    Cited by:

    1. Jean-Philippe Aguilar & Cyril Coste & Jan Korbel, 2017. "Series representation of the pricing formula for the European option driven by space-time fractional diffusion," Papers 1712.04990, arXiv.org, revised Oct 2018.

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