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Resemblance of the power-law scaling behavior of a non-Markovian and nonlinear point processes

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  • Aleksejus Kononovicius
  • Rytis Kazakeviv{c}ius
  • Bronislovas Kaulakys

Abstract

We analyze the statistical properties of a temporal point process driven by a confined fractional Brownian motion. The event count distribution and power spectral density of this non--Markovian point process exhibit power--law scaling. We show that a nonlinear Markovian point process can reproduce the same scaling behavior. This result indicates a possible link between nonlinearity and apparent non--Markovian behavior.

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  • Aleksejus Kononovicius & Rytis Kazakeviv{c}ius & Bronislovas Kaulakys, 2022. "Resemblance of the power-law scaling behavior of a non-Markovian and nonlinear point processes," Papers 2205.07563, arXiv.org, revised Jul 2022.
    • Handle: RePEc:arx:papers:2205.07563
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    References listed on IDEAS

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    1. Fred Espen Benth & Jūratė Šaltytė Benth, 2012. "Modeling and Pricing in Financial Markets for Weather Derivatives," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8457, August.
    2. Vygintas Gontis & Bronislovas Kaulakys, 2003. "Multiplicative point process as a model of trading activity," Papers cond-mat/0303089, arXiv.org, revised Dec 2004.
    3. Fred Espen Benth & Jūratė Šaltytė Benth, 2012. "Extensions of temperature and wind speed models," World Scientific Book Chapters, in: Modeling and Pricing in Financial Markets for Weather Derivatives, chapter 6, pages 139-155, World Scientific Publishing Co. Pte. Ltd..
    4. V. Gontis & A. Kononovicius, 2014. "Consentaneous agent-based and stochastic model of the financial markets," Papers 1403.1574, arXiv.org, revised Jul 2014.
    5. Li, Zhongping & Cui, Lirong & Chen, Jianhui, 2018. "Traffic accident modelling via self-exciting point processes," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 312-320.
    6. Giraitis, Liudas & Robinson, Peter M. & Surgailis, Donatas, 2000. "A model for long memory conditional heteroscedasticity," LSE Research Online Documents on Economics 299, London School of Economics and Political Science, LSE Library.
    7. Jaume Masoliver & Katja Lindenberg, 2017. "Continuous time persistent random walk: a review and some generalizations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(6), pages 1-13, June.
    8. 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.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. Vygintas Gontis & Aleksejus Kononovicius, 2014. "Consentaneous Agent-Based and Stochastic Model of the Financial Markets," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-12, July.
    11. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    12. Kononovicius, A. & Gontis, V., 2012. "Agent based reasoning for the non-linear stochastic models of long-range memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1309-1314.
    13. Akinlar, M.A. & Inc, Mustafa & Gómez-Aguilar, J.F. & Boutarfa, B., 2020. "Solutions of a disease model with fractional white noise," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    14. Fred Espen Benth & Jūratė Šaltytė Benth, 2012. "Financial markets for weather," World Scientific Book Chapters, in: Modeling and Pricing in Financial Markets for Weather Derivatives, chapter 1, pages 1-13, World Scientific Publishing Co. Pte. Ltd..
    15. Ben Hambly & Jasdeep Kalsi & James Newbury, 2020. "Limit Order Books, Diffusion Approximations and Reflected SPDEs: From Microscopic to Macroscopic Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(1-2), pages 132-170, July.
    16. Liudas Giraitis & Remigijus Leipus & Donatas Surgailis, 2007. "Recent Advances in ARCH Modelling," Springer Books, in: Gilles Teyssière & Alan P. Kirman (ed.), Long Memory in Economics, pages 3-38, Springer.
    17. Michelitsch, Thomas M. & Riascos, Alejandro P., 2020. "Continuous time random walk and diffusion with generalized fractional Poisson process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    18. Gontis, V. & Kaulakys, B., 2004. "Multiplicative point process as a model of trading activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 505-514.
    19. Gontis, V. & Ruseckas, J. & Kononovičius, A., 2010. "A long-range memory stochastic model of the return in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 100-106.
    20. Giraitis, Liudas & Robinson, Peter & Surgailis, Donatas, 2000. "A model for long memory conditional heteroscedasticity," LSE Research Online Documents on Economics 2103, London School of Economics and Political Science, LSE Library.
    21. Kiyoshi Kanazawa & Didier Sornette, 2021. "Ubiquitous power law scaling in nonlinear self-excited Hawkes processes," Papers 2102.00242, arXiv.org, revised Oct 2021.
    22. Kaulakys, Bronislovas & Ruseckas, Julius & Gontis, Vygintas & Alaburda, Miglius, 2006. "Nonlinear stochastic models of 1/f noise and power-law distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 217-221.
    23. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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