IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v149y2022icp75-106.html
   My bibliography  Save this article

Statistical analysis for stationary time series at extreme levels: New estimators for the limiting cluster size distribution

Author

Listed:
  • Bücher, Axel
  • Jennessen, Tobias

Abstract

The serial dependence of a stationary time series at extreme levels may be captured by the limiting cluster size distribution. New estimators based on a blocks declustering scheme are proposed and analyzed both theoretically and by means of a large-scale simulation study. A sliding blocks version of the estimators is shown to outperform a disjoint blocks version. In contrast to some competitors from the literature, the estimators only depend on one tuning parameter to be chosen by the statistician.

Suggested Citation

  • Bücher, Axel & Jennessen, Tobias, 2022. "Statistical analysis for stationary time series at extreme levels: New estimators for the limiting cluster size distribution," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 75-106.
    • Handle: RePEc:eee:spapps:v:149:y:2022:i:c:p:75-106
    DOI: 10.1016/j.spa.2022.03.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414922000606
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2022.03.004?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. Kulik, Rafał & Soulier, Philippe & Wintenberger, Olivier, 2019. "The tail empirical process of regularly varying functions of geometrically ergodic Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4209-4238.
    2. Drees, Holger & Segers, Johan & Warchol, Michal, 2015. "Statistics for Tail Processes of Markov Chains," LIDAM Reprints ISBA 2015023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Davis, Richard A. & Drees, Holger & Segers, Johan & WarchoÅ‚, MichaÅ‚, 2018. "Inference on the tail process with application to financial time series modelling," LIDAM Reprints ISBA 2018022, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Basrak, Bojan & Segers, Johan, 2009. "Regularly varying multivariate time series," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1055-1080, April.
    5. Hsing, Tailen, 1991. "Estimating the parameters of rare events," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 117-139, February.
    6. Davis, Richard A. & Drees, Holger & Segers, Johan & Warchoł, Michał, 2018. "Inference on the tail process with application to financial time series modeling," Journal of Econometrics, Elsevier, vol. 205(2), pages 508-525.
    7. de Haan, Laurens & Resnick, Sidney I. & Rootzén, Holger & de Vries, Casper G., 1989. "Extremal behaviour of solutions to a stochastic difference equation with applications to arch processes," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 213-224, August.
    8. Janssens, Anja & Segers, Johan, 2015. "Markov tail chains," LIDAM Reprints ISBA 2015010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Davis, Richard & Drees, Holger & Segers, Johan & Warchol, Michal, 2018. "Inference on the tail process with application to financial time series modelling," LIDAM Discussion Papers ISBA 2018002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Christopher A. T. Ferro & Johan Segers, 2003. "Inference for clusters of extreme values," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 545-556, May.
    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. Drees, Holger & Janßen, Anja & Neblung, Sebastian, 2021. "Cluster based inference for extremes of time series," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 1-33.
    2. Buriticá, Gloria & Mikosch, Thomas & Wintenberger, Olivier, 2023. "Large deviations of ℓp-blocks of regularly varying time series and applications to cluster inference," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 68-101.
    3. Gloria Buriticá & Philippe Naveau, 2023. "Stable sums to infer high return levels of multivariate rainfall time series," Environmetrics, John Wiley & Sons, Ltd., vol. 34(4), June.
    4. Damek, Ewa & Mikosch, Thomas & Zhao, Yuwei & Zienkiewicz, Jacek, 2023. "Whittle estimation based on the extremal spectral density of a heavy-tailed random field," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 232-267.
    5. Zhao, Zifeng & Zhang, Zhengjun & Chen, Rong, 2018. "Modeling maxima with autoregressive conditional Fréchet model," Journal of Econometrics, Elsevier, vol. 207(2), pages 325-351.
    6. Pedro Henrique Melo Albuquerque & Yaohao Peng & João Pedro Fontoura da Silva, 2022. "Making the whole greater than the sum of its parts: A literature review of ensemble methods for financial time series forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(8), pages 1701-1724, December.
    7. Davis, Richard & Drees, Holger & Segers, Johan & Warchol, Michal, 2018. "Inference on the tail process with application to financial time series modelling," LIDAM Discussion Papers ISBA 2018002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Davis, Richard & Holger, Drees & Segers, Johan & Warchol, Michal, 2016. "Modeling serial extremal dependence," LIDAM Discussion Papers ISBA 2016016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Rasmus Pedersen & Olivier Wintenberger, 2017. "On the tail behavior of a class of multivariate conditionally heteroskedastic processes," Papers 1701.05091, arXiv.org, revised Dec 2017.
    10. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    11. A. P. Martins & J. R. Sebastião, 2019. "Methods for estimating the upcrossings index: improvements and comparison," Statistical Papers, Springer, vol. 60(4), pages 1317-1347, August.
    12. J. Sebastião & A. Martins & H. Ferreira & L. Pereira, 2013. "Estimating the upcrossings index," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(4), pages 549-579, November.
    13. Segers, Johan & Zhao, Yuwei & Meinguet, Thomas, 2016. "Radial-angular decomposition of regularly varying time series in star-shaped metric spaces," LIDAM Discussion Papers ISBA 2016017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Jondeau, Eric & Rockinger, Michael, 2003. "Testing for differences in the tails of stock-market returns," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 559-581, December.
    15. Jalal, Amine & Rockinger, Michael, 2008. "Predicting tail-related risk measures: The consequences of using GARCH filters for non-GARCH data," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 868-877, December.
    16. Tian, Shuairu & Hamori, Shigeyuki, 2015. "Modeling interest rate volatility: A Realized GARCH approach," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 158-171.
    17. Davis, Richard A. & Mikosch, Thomas & Zhao, Yuwei, 2013. "Measures of serial extremal dependence and their estimation," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2575-2602.
    18. Jose Olmo, 2015. "A New Family of Consistent and Asymptotically-Normal Estimators for the Extremal Index," Econometrics, MDPI, vol. 3(3), pages 1-21, August.
    19. John Galbraith & Serguei Zernov, 2009. "Extreme dependence in the NASDAQ and S&P 500 composite indexes," Applied Financial Economics, Taylor & Francis Journals, vol. 19(13), pages 1019-1028.
    20. janssen, Anja & Segers, Johan, 2013. "Markov Tail Chains," LIDAM Discussion Papers ISBA 2013017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    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:spapps:v:149:y:2022:i:c:p:75-106. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.