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Superstatistical fluctuations in time series: Applications to share-price dynamics and turbulence

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  • Erik Van der Straeten
  • Christian Beck

Abstract

We report a general technique to study a given experimental time series with superstatistics. Crucial for the applicability of the superstatistics concept is the existence of a parameter $\beta$ that fluctuates on a large time scale as compared to the other time scales of the complex system under consideration. The proposed method extracts the main superstatistical parameters out of a given data set and examines the validity of the superstatistical model assumptions. We test the method thoroughly with surrogate data sets. Then the applicability of the superstatistical approach is illustrated using real experimental data. We study two examples, velocity time series measured in turbulent Taylor-Couette flows and time series of log returns of the closing prices of some stock market indices.

Suggested Citation

  • Erik Van der Straeten & Christian Beck, 2009. "Superstatistical fluctuations in time series: Applications to share-price dynamics and turbulence," Papers 0901.2271, arXiv.org, revised Sep 2009.
    • Handle: RePEc:arx:papers:0901.2271
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    Cited by:

    1. Lemmens, D. & Liang, L.Z.J. & Tempere, J. & De Schepper, A., 2010. "Pricing bounds for discrete arithmetic Asian options under Lévy models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5193-5207.
    2. dos Santos, Maike A.F. & Junior, Luiz Menon, 2021. "Random diffusivity models for scaled Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Marian Gidea & Yuri Katz, 2017. "Topological Data Analysis of Financial Time Series: Landscapes of Crashes," Papers 1703.04385, arXiv.org, revised Apr 2017.
    4. Yusuke Uchiyama & Takanori Kadoya, 2018. "Superstatistics with cut-off tails for financial time series," Papers 1809.04775, arXiv.org.
    5. Kosun, Caglar & Ozdemir, Serhan, 2016. "A superstatistical model of vehicular traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 466-475.
    6. Geoffrey Ducournau, 2021. "Bayesian inference and superstatistics to describe long memory processes of financial time series," Papers 2105.04171, arXiv.org.
    7. Devi, Sandhya, 2021. "Asymmetric Tsallis distributions for modeling financial market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    8. Sandhya Devi, 2021. "Asymmetric Tsallis distributions for modelling financial market dynamics," Papers 2102.04532, arXiv.org.
    9. Kosun, Caglar & Ozdemir, Serhan, 2017. "Determining the complexity of multi-component conformal systems: A platoon-based approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 688-695.
    10. Xu, Dan & Beck, Christian, 2016. "Transition from lognormal to χ2-superstatistics for financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 173-183.
    11. Katz, Yuri A. & Biem, Alain, 2021. "Time-resolved topological data analysis of market instabilities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 571(C).

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