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Nonextensive Statistical Mechanics Distributions And Dynamics Of Financial Observables From The Nonlinear Stochastic Differential Equations

Author

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  • JULIUS RUSECKAS

    (Institute of Theoretical Physics and Astronomy, Vilnius University, A. Goštauto 12, LT-01108 Vilnius, Lithuania)

  • VYGINTAS GONTIS

    (Institute of Theoretical Physics and Astronomy, Vilnius University, A. Goštauto 12, LT-01108 Vilnius, Lithuania)

  • BRONISLOVAS KAULAKYS

    (Institute of Theoretical Physics and Astronomy, Vilnius University, A. Goštauto 12, LT-01108 Vilnius, Lithuania)

Abstract

We present nonlinear stochastic differential equations, generating processes with theq-exponential andq-Gaussian distributions of the observables, i.e. with the long-range power-law autocorrelations and1/fβpower spectral density. Similarly, the Tsallisq-distributions may be obtained in the superstatistical framework as a superposition of different local dynamics at different time intervals. In such approach, the average of the stochastic variable is generated by the nonlinear stochastic process, while the local distribution of the signal is exponential or Gaussian one, conditioned by the slow average. Further we analyze relevance of the generalized and adapted equations for modeling the financial processes. We model the inter-trade durations, the trading activity and the normalized return using the superstatistical approaches with the exponential and normal distributions of the local signals driven by the nonlinear stochastic process.

Suggested Citation

  • Julius Ruseckas & Vygintas Gontis & Bronislovas Kaulakys, 2012. "Nonextensive Statistical Mechanics Distributions And Dynamics Of Financial Observables From The Nonlinear Stochastic Differential Equations," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 15(supp0), pages 1-13.
    • Handle: RePEc:wsi:acsxxx:v:15:y:2012:i:supp0:n:s0219525912500737
    DOI: 10.1142/S0219525912500737
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    References listed on IDEAS

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    1. Lax, Melvin & Cai, Wei & Xu, Min, 2006. "Random Processes in Physics and Finance," OUP Catalogue, Oxford University Press, number 9780198567769.
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    Citations

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    Cited by:

    1. Kononovicius, Aleksejus & Ruseckas, Julius, 2019. "Order book model with herd behavior exhibiting long-range memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 171-191.
    2. Vygintas Gontis & Aleksejus Kononovicius, 2019. "Bessel-like birth-death process," Papers 1904.13064, arXiv.org, revised Oct 2019.
    3. Gontis, V. & Kononovicius, A., 2020. "Bessel-like birth–death process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    4. Aleksejus Kononovicius & Julius Ruseckas, 2018. "Order book model with herd behavior exhibiting long-range memory," Papers 1809.02772, arXiv.org, revised Apr 2019.
    5. Rytis Kazakevicius & Aleksejus Kononovicius & Bronislovas Kaulakys & Vygintas Gontis, 2021. "Understanding the nature of the long-range memory phenomenon in socioeconomic systems," Papers 2108.02506, arXiv.org, revised Aug 2021.

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