IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v93y2014icp46-57.html
   My bibliography  Save this article

Extremal behavior of pMAX processes

Author

Listed:
  • Ferreira, Helena
  • Ferreira, Marta

Abstract

The well-known M4 processes of Smith and Weissman are very flexible models for asymptotically dependent multivariate data. Extended M4 of Heffernan et al. allows to also account for asymptotic independence. In this paper we introduce a more general multivariate model comprising asymptotic dependence and independence, which has the extended M4 class as a particular case. We study properties of the proposed model. In particular, we compute the multivariate extremal index, tail dependence and extremal coefficients.

Suggested Citation

  • Ferreira, Helena & Ferreira, Marta, 2014. "Extremal behavior of pMAX processes," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 46-57.
    • Handle: RePEc:eee:stapro:v:93:y:2014:i:c:p:46-57
    DOI: 10.1016/j.spl.2014.06.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715214002119
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2014.06.009?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. Anthony W. Ledford & Jonathan A. Tawn, 1997. "Modelling Dependence within Joint Tail Regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 475-499.
    2. Marta Ferreira & Helena Ferreira, 2012. "On extremal dependence: some contributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 566-583, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Martins, Ana Paula & Ferreira, Helena & Ferreira, Marta, 2022. "A new random field on lattices," Statistics & Probability Letters, Elsevier, vol. 186(C).
    2. Marta Ferreira & Helena Ferreira, 2017. "Analyzing the Gaver—Lewis Pareto Process under an Extremal Perspective," Risks, MDPI, vol. 5(3), pages 1-12, June.
    3. Helena Ferreira & Marta Ferreira, 2021. "Tail dependence and smoothness of time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 198-210, March.

    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. Holger Drees, 2012. "Extreme value analysis of actuarial risks: estimation and model validation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 225-264, June.
    2. Drees, Holger & Müller, Peter, 2008. "Fitting and validation of a bivariate model for large claims," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 638-650, April.
    3. Ibrahim Ergen, 2014. "Tail dependence and diversification benefits in emerging market stocks: an extreme value theory approach," Applied Economics, Taylor & Francis Journals, vol. 46(19), pages 2215-2227, July.
    4. Li, Feng & Kang, Yanfei, 2018. "Improving forecasting performance using covariate-dependent copula models," International Journal of Forecasting, Elsevier, vol. 34(3), pages 456-476.
    5. Liu, Aiai & Hou, Yanxi & Peng, Liang, 2015. "Interval estimation for a measure of tail dependence," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 294-305.
    6. Brook T. Russell & Whitney K. Huang, 2021. "Modeling short‐ranged dependence in block extrema with application to polar temperature data," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    7. Moore, Kyle & Zhou, Chen, 2014. "The determinants of systemic importance," LSE Research Online Documents on Economics 59289, London School of Economics and Political Science, LSE Library.
    8. Xiangying Meng & Xianhua Wei, 2018. "Systematic Correlation is Priced as Risk Factor," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 8(6), pages 1-2.
    9. Qiurong Cui & Zhengjun Zhang, 2018. "Max-Linear Competing Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 62-74, January.
    10. Keef, Caroline & Papastathopoulos, Ioannis & Tawn, Jonathan A., 2013. "Estimation of the conditional distribution of a multivariate variable given that one of its components is large: Additional constraints for the Heffernan and Tawn model," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 396-404.
    11. Fang Zhang & Zhengjun Zhang, 2020. "The tail dependence of the carbon markets: The implication of portfolio management," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-17, August.
    12. Ferreira Helena & Ferreira Marta, 2022. "The stopped clock model," Dependence Modeling, De Gruyter, vol. 10(1), pages 48-57, January.
    13. Michael Falk & René Michel, 2006. "Testing for Tail Independence in Extreme Value models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 261-290, June.
    14. 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.
    15. Goegebeur, Yuri & Guillou, Armelle & Ho, Nguyen Khanh Le & Qin, Jing, 2020. "Robust nonparametric estimation of the conditional tail dependence coefficient," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    16. Mikael Escobar-Bach & Yuri Goegebeur & Armelle Guillou & Alexandre You, 2017. "Bias-corrected and robust estimation of the bivariate stable tail dependence function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 284-307, June.
    17. Christophe Dutang & Yuri Goegebeur & Armelle Guillou, 2016. "Robust and bias-corrected estimation of the probability of extreme failure sets," Post-Print hal-01616187, HAL.
    18. A. Abu-Awwad & V. Maume-Deschamps & P. Ribereau, 2020. "Fitting spatial max-mixture processes with unknown extremal dependence class: an exploratory analysis tool," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 479-522, June.
    19. Paola Bortot & Carlo Gaetan, 2016. "Latent Process Modelling of Threshold Exceedances in Hourly Rainfall Series," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 531-547, September.

    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:stapro:v:93:y:2014:i:c:p:46-57. 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/622892/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.