IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v20y2018i2d10.1007_s11009-017-9573-4.html
   My bibliography  Save this article

Level Hitting Probabilities and Extremal Indexes for Some Particular Dynamical Systems

Author

Listed:
  • George Haiman

Abstract

We establish an exact formula for the distribution of the partial maximum sequence generated by the stationary process obtained by iterations of the Rényi map x → βx mod 1, β = 2, 3, .... We thus obtain a simple proof of some asymptotic behaviour of the extremes and the values of the extremal index. A numerical application is presented.

Suggested Citation

  • George Haiman, 2018. "Level Hitting Probabilities and Extremal Indexes for Some Particular Dynamical Systems," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 553-562, June.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:2:d:10.1007_s11009-017-9573-4
    DOI: 10.1007/s11009-017-9573-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-017-9573-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-017-9573-4?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. Freitas, Ana Cristina Moreira & Freitas, Jorge Milhazes, 2008. "On the link between dependence and independence in extreme value theory for dynamical systems," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1088-1093, July.
    2. Yannick Malevergne & Vladilen Pisarenko & Didier Sornette, 2006. "On the Power of Generalized Extreme Value (GEV) and Generalized Pareto Distribution (GPD) Estimators for Empirical Distributions of Stock Returns," Post-Print hal-02311834, HAL.
    3. Haiman, George, 2003. "Extreme values of the tent map process," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 451-456, December.
    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. Freitas, Ana Cristina Moreira, 2009. "Statistics of the maximum for the tent map," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 604-608.
    2. Salhi, Khaled & Deaconu, Madalina & Lejay, Antoine & Champagnat, Nicolas & Navet, Nicolas, 2016. "Regime switching model for financial data: Empirical risk analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 148-157.
    3. 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).
    4. V. F. Pisarenko & D. Sornette, 2004. "New statistic for financial return distributions: power-law or exponential?," Papers physics/0403075, arXiv.org.
    5. Freitas, Ana Cristina Moreira & Freitas, Jorge Milhazes, 2008. "On the link between dependence and independence in extreme value theory for dynamical systems," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1088-1093, July.
    6. Freitas, Ana Cristina Moreira & Freitas, Jorge Milhazes & Todd, Mike, 2015. "Speed of convergence for laws of rare events and escape rates," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1653-1687.
    7. Matteo Gentilucci & Alessandro Rossi & Niccolò Pelagagge & Domenico Aringoli & Maurizio Barbieri & Gilberto Pambianchi, 2023. "GEV Analysis of Extreme Rainfall: Comparing Different Time Intervals to Analyse Model Response in Terms of Return Levels in the Study Area of Central Italy," Sustainability, MDPI, vol. 15(15), pages 1-25, July.
    8. Fernandes, José L. B. & Hasman, Augusto & Peña, Juan Ignacio, 2006. "Risk premium: insights over the threshold," DEE - Working Papers. Business Economics. WB wb062808, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    9. Bertrand B. Maillet & Jean-Philippe R. M�decin, 2010. "Extreme Volatilities, Financial Crises and L-moment Estimations of Tail-indexes," Working Papers 2010_10, Department of Economics, University of Venice "Ca' Foscari".
    10. Gu, Gao-Feng & Chen, Wei & Zhou, Wei-Xing, 2008. "Empirical distributions of Chinese stock returns at different microscopic timescales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 495-502.
    11. Livieri, Giulia & Lillo, Fabrizio & Marmi, Stefano & Solomko, Anton & Vaienti, Sandro, 2023. "Unimodal maps perturbed by heteroscedastic noise: an application to a financial systems," LSE Research Online Documents on Economics 120290, London School of Economics and Political Science, LSE Library.
    12. Freitas, Ana Cristina Moreira & Freitas, Jorge Milhazes & Todd, Mike & Vaienti, Sandro, 2016. "Rare events for the Manneville–Pomeau map," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3463-3479.
    13. Rakhee Dinubhai Patel & Frederic Paik Schoenberg, 2011. "A graphical test for local self-similarity in univariate data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2547-2562, January.
    14. Montshioa, Keitumetse & Muteba Mwamba, John Weirstrass & Bonga-Bonga, Lumengo, 2021. "Asset allocation in extreme market conditions: a comparative analysis between developed and emerging economies," MPRA Paper 106248, University Library of Munich, Germany.
    15. Faranda, Davide & Freitas, Jorge Milhazes & Guiraud, Pierre & Vaienti, Sandro, 2015. "Sampling local properties of attractors via Extreme Value Theory," Chaos, Solitons & Fractals, Elsevier, vol. 74(C), pages 55-66.
    16. Bonga-Bonga, Lumengo & Montshioa, Keitumetse, 2024. "Navigating extreme market fluctuations: asset allocation strategies in developed vs. emerging economies," MPRA Paper 119910, University Library of Munich, Germany.
    17. Angel, Omer & Matzavinos, Anastasios & Roitershtein, Alexander, 2019. "Limit theorem for the Robin Hood game," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 9-15.
    18. Marcin Wk{a}torek & Jaros{l}aw Kwapie'n & Stanis{l}aw Dro.zd.z, 2021. "Financial Return Distributions: Past, Present, and COVID-19," Papers 2107.06659, arXiv.org.

    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:spr:metcap:v:20:y:2018:i:2:d:10.1007_s11009-017-9573-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.