IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v183y2024ics096007792400479x.html
   My bibliography  Save this article

Effect of nonlinearity of discrete Langevin model on behavior of extremes in generated time series

Author

Listed:
  • Czechowski, Zbigniew
  • Telesca, Luciano

Abstract

In this work we analyze the influence of nonlinearity on the behavior of extremal values of time series generated by two discrete Langevin models: fixing the diffusion function in the first (M1), the probability distribution function in the second (M2). The extremes were generated by applying the run theory. A mathematical relationship was found between nonlinearity of models and means and distributions of run lengths and inter-extreme times as well as with the clustering of extremes. Furthermore, the Allan factor curves of the extremes suggest that the sequences of extremes are fractal for timescales up to the mean inter-extreme time. Our main findings are that the variation of the nonlinearity parameter in model M1 (leading to the increase of the distribution tail length) can cause a significant variation of the extreme characteristics and an increase of the clustering while the variation of the nonlinearity parameter in model M2 (with fixed distribution) has a little effect on extremes.

Suggested Citation

  • Czechowski, Zbigniew & Telesca, Luciano, 2024. "Effect of nonlinearity of discrete Langevin model on behavior of extremes in generated time series," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s096007792400479x
    DOI: 10.1016/j.chaos.2024.114927
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792400479X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.114927?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Telesca, Luciano & Czechowski, Zbigniew, 2012. "Discriminating geoelectrical signals measured in seismic and aseismic areas by using Ito models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 809-818.
    2. Xu, Pengfei & Gong, Xulu & Wang, Haotian & Li, Yiwei & Liu, Di, 2023. "A study of stochastic resonance in tri-stable generalized Langevin system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    3. Bunde, Armin & F. Eichner, Jan & Havlin, Shlomo & Kantelhardt, Jan W., 2003. "The effect of long-term correlations on the return periods of rare events," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(1), pages 1-7.
    4. Czechowski, Zbigniew & Rozmarynowska, Aneta, 2008. "The importance of the privilege for appearance of inverse-power solutions in Ito equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5403-5416.
    5. M. S. Santhanam & Holger Kantz, 2008. "Return interval distribution of extreme events and long term memory," Papers 0803.1706, arXiv.org.
    6. Czechowski, Zbigniew & Telesca, Luciano, 2011. "The construction of an Ito model for geoelectrical signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2511-2519.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Karain, Wael I., 2019. "Investigating large-amplitude protein loop motions as extreme events using recurrence interval analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 1-10.
    2. Pushpa Dissanayake & Teresa Flock & Johanna Meier & Philipp Sibbertsen, 2021. "Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights," Mathematics, MDPI, vol. 9(21), pages 1-33, November.
    3. Xie, Wen-Jie & Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2014. "Extreme value statistics and recurrence intervals of NYMEX energy futures volatility," Economic Modelling, Elsevier, vol. 36(C), pages 8-17.
    4. Czechowski, Zbigniew & Telesca, Luciano, 2013. "Construction of a Langevin model from time series with a periodical correlation function: Application to wind speed data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5592-5603.
    5. Ren, Fei & Gu, Gao-Feng & Zhou, Wei-Xing, 2009. "Scaling and memory in the return intervals of realized volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(22), pages 4787-4796.
    6. Livina, V. & Tuzov, S. & Havlin, S. & Bunde, A., 2005. "Recurrence intervals between earthquakes strongly depend on history," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 591-595.
    7. M. Ghil & Pascal Yiou & Stéphane Hallegatte & B. D. Malamud & P. Naveau & A. Soloviev & P. Friederichs & V. Keilis-Borok & D. Kondrashov & V. Kossobokov & O. Mestre & C. Nicolis & H. W. Rust & P. Sheb, 2011. "Extreme events: dynamics, statistics and prediction," Post-Print hal-00716514, HAL.
    8. Zhi-Qiang Jiang & Gang-Jin Wang & Askery Canabarro & Boris Podobnik & Chi Xie & H. Eugene Stanley & Wei-Xing Zhou, 2018. "Short term prediction of extreme returns based on the recurrence interval analysis," Quantitative Finance, Taylor & Francis Journals, vol. 18(3), pages 353-370, March.
    9. Li, Wei-Zhen & Zhai, Jin-Rui & Jiang, Zhi-Qiang & Wang, Gang-Jin & Zhou, Wei-Xing, 2022. "Predicting tail events in a RIA-EVT-Copula framework," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    10. Xing, Yani & Wang, Jun, 2019. "Statistical volatility duration and complexity of financial dynamics on Sierpinski gasket lattice percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 234-247.
    11. Zhu, Jinjie & Zhao, Feng & Li, Yang & Liu, Xianbin, 2024. "Rotational stochastic resonance in multistable systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 634(C).
    12. Batac, Rene & Longjas, Anthony & Monterola, Christopher, 2012. "Statistical distributions of avalanche size and waiting times in an inter-sandpile cascade model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 616-624.
    13. Ren, Fei & Guo, Liang & Zhou, Wei-Xing, 2009. "Statistical properties of volatility return intervals of Chinese stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 881-890.
    14. Picoli, Sergio & Bombo, Giorgio & Santos, Edenize S.D. & Deprá, Pedro P. & Mendes, Renio S., 2022. "Characterizing postural sway signals by the analysis of zero-crossing patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    15. Chicheportiche, Rémy & Chakraborti, Anirban, 2017. "A model-free characterization of recurrences in stationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 312-318.
    16. Ribeiro, H.V. & Mendes, R.S. & Lenzi, E.K. & Belancon, M.P. & Malacarne, L.C., 2011. "On the dynamics of bubbles in boiling water," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 178-183.
    17. Telesca, Luciano & Czechowski, Zbigniew, 2012. "Discriminating geoelectrical signals measured in seismic and aseismic areas by using Ito models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 809-818.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s096007792400479x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.