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Transition from lognormal to χ2-superstatistics for financial time series

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  • Xu, Dan
  • Beck, Christian

Abstract

Share price returns on different time scales can be well modelled by a superstatistical dynamics. Here we provide an investigation which type of superstatistics is most suitable to properly describe share price dynamics on various time scales. It is shown that while χ2-superstatistics works well on a time scale of days, on a much smaller time scale of minutes the price changes are better described by lognormal superstatistics. The system dynamics thus exhibits a transition from lognormal to χ2 superstatistics as a function of time scale. We discuss a more general model interpolating between both statistics which fits the observed data very well. We also present results on correlation functions of the extracted superstatistical volatility parameter, which exhibits exponential decay for returns on large time scales, whereas for returns on small time scales there are long-range correlations and power-law decay.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:453:y:2016:i:c:p:173-183
    DOI: 10.1016/j.physa.2016.02.057
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    Cited by:

    1. Markelov, Oleg & Nguyen Duc, Viet & Bogachev, Mikhail, 2017. "Statistical modeling of the Internet traffic dynamics: To which extent do we need long-term correlations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 48-60.
    2. Sandhya Devi, 2021. "Asymmetric Tsallis distributions for modelling financial market dynamics," Papers 2102.04532, arXiv.org.
    3. Arias-Calluari, Karina & Najafi, Morteza. N. & Harré, Michael S. & Tang, Yaoyue & Alonso-Marroquin, Fernando, 2022. "Testing stationarity of the detrended price return in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    4. Karina Arias-Calluari & Morteza. N. Najafi & Michael S. Harr'e & Fernando Alonso-Marroquin, 2019. "Stationarity of the detrended price return in stock markets," Papers 1910.01034, arXiv.org, revised Aug 2020.
    5. Yusuke Uchiyama & Takanori Kadoya, 2018. "Superstatistics with cut-off tails for financial time series," Papers 1809.04775, arXiv.org.
    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).

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