IDEAS home Printed from https://ideas.repec.org/a/bla/jorssc/v58y2009i1p25-45.html
   My bibliography  Save this article

Modelling non‐stationary extremes with application to surface level ozone

Author

Listed:
  • Emma F. Eastoe
  • Jonathan A. Tawn

Abstract

Summary. Statistical methods for modelling extremes of stationary sequences have received much attention. The most common method is to model the rate and size of exceedances of some high constant threshold; the size of exceedances is modelled by using a generalized Pareto distribution. Frequently, data sets display non‐stationarity; this is especially common in environmental applications. The ozone data set that is presented here is an example of such a data set. Surface level ozone levels display complex seasonal patterns and trends due to the mechanisms that are involved in ozone formation. The standard methods of modelling the extremes of a non‐stationary process focus on retaining a constant threshold but using covariate models in the rate and generalized Pareto distribution parameters. We suggest an alternative approach that uses preprocessing methods to model the non‐stationarity in the body of the process and then uses standard methods to model the extremes of the preprocessed data. We illustrate both the standard and the preprocessing methods by using a simulation study and a study of the ozone data. We suggest that the preprocessing method gives a model that better incorporates the underlying mechanisms that generate the process, produces a simpler and more efficient fit and allows easier computation.

Suggested Citation

  • Emma F. Eastoe & Jonathan A. Tawn, 2009. "Modelling non‐stationary extremes with application to surface level ozone," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(1), pages 25-45, February.
    • Handle: RePEc:bla:jorssc:v:58:y:2009:i:1:p:25-45
    DOI: 10.1111/j.1467-9876.2008.00638.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9876.2008.00638.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9876.2008.00638.x?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
    ---><---

    References listed on IDEAS

    as
    1. V. Chavez‐Demoulin & A. C. Davison, 2005. "Generalized additive modelling of sample extremes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 207-222, January.
    2. Janet E. Heffernan & Jonathan A. Tawn, 2004. "A conditional approach for multivariate extreme values (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 497-546, August.
    3. A. C. Davison & N. I. Ramesh, 2000. "Local likelihood smoothing of sample extremes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 191-208.
    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. Nurulkamal Masseran & Muhammad Aslam Mohd Safari, 2021. "Mixed POT-BM Approach for Modeling Unhealthy Air Pollution Events," IJERPH, MDPI, vol. 18(13), pages 1-17, June.
    2. Anna Maria Barlow & Chris Sherlock & Jonathan Tawn, 2020. "Inference for extreme values under threshold‐based stopping rules," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 765-789, August.
    3. Jonathan Jalbert & Anne-Catherine Favre & Claude Bélisle & Jean-François Angers, 2017. "A spatiotemporal model for extreme precipitation simulated by a climate model, with an application to assessing changes in return levels over North America," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(5), pages 941-962, November.
    4. Rishikesh Yadav & Raphaël Huser & Thomas Opitz, 2021. "Spatial hierarchical modeling of threshold exceedances using rate mixtures," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    5. Julien Hambuckers & Marie Kratz & Antoine Usseglio-Carleve, 2023. "Efficient Estimation In Extreme Value Regression Models Of Hedge Fund Tail Risks," Working Papers hal-04090916, HAL.
    6. Julien Hambuckers & Marie Kratz & Antoine Usseglio-Carleve, 2023. "Efficient Estimation in Extreme Value Regression Models of Hedge Fund Tail Risks," Papers 2304.06950, arXiv.org.
    7. Sigauke, Caston & Bere, Alphonce, 2017. "Modelling non-stationary time series using a peaks over threshold distribution with time varying covariates and threshold: An application to peak electricity demand," Energy, Elsevier, vol. 119(C), pages 152-166.
    8. C J Scarrott & A MacDonald, 2010. "Extreme-value-model-based risk assessment for nuclear reactors," Journal of Risk and Reliability, , vol. 224(4), pages 239-252, December.
    9. Ross Towe & Jonathan Tawn & Emma Eastoe & Rob Lamb, 2020. "Modelling the Clustering of Extreme Events for Short-Term Risk Assessment," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(1), pages 32-53, March.
    10. M. de Carvalho & K. F. Turkman & A. Rua, 2013. "Dynamic threshold modelling and the US business cycle," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(4), pages 535-550, August.
    11. M. Carvalho & S. Pereira & P. Pereira & P. Zea Bermudez, 2022. "An Extreme Value Bayesian Lasso for the Conditional Left and Right Tails," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 222-239, June.
    12. Tong Siu Tung Wong & Wai Keung Li, 2015. "Extreme values identification in regression using a peaks-over-threshold approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(3), pages 566-576, March.
    13. 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.
    14. Daniela Castro Camilo & Miguel de Carvalho & Jennifer Wadsworth, 2017. "Time-Varying Extreme Value Dependence with Application to Leading European Stock Markets," Papers 1709.01198, arXiv.org.
    15. Fernando Nascimento & Dani Gamerman & Hedibert Lopes, 2016. "Time-varying extreme pattern with dynamic models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 131-149, March.
    16. C. J. R. Murphy‐Barltrop & J. L. Wadsworth & E. F. Eastoe, 2023. "New estimation methods for extremal bivariate return curves," Environmetrics, John Wiley & Sons, Ltd., vol. 34(5), August.

    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. Ahmad Aboubacrène Ag & Deme El Hadji & Diop Aliou & Girard Stéphane, 2019. "Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions," Dependence Modeling, De Gruyter, vol. 7(1), pages 394-417, January.
    2. Daniela Castro Camilo & Miguel de Carvalho & Jennifer Wadsworth, 2017. "Time-Varying Extreme Value Dependence with Application to Leading European Stock Markets," Papers 1709.01198, arXiv.org.
    3. Daouia, Abdelaati & Gardes, Laurent & Girard, Stephane, 2011. "On kernel smoothing for extremal quantile regression," LIDAM Discussion Papers ISBA 2011031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Bousebata, Meryem & Enjolras, Geoffroy & Girard, Stéphane, 2023. "Extreme partial least-squares," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    5. Laurini, Fabrizio & Pauli, Francesco, 2009. "Smoothing sample extremes: The mixed model approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3842-3854, September.
    6. Gardes, Laurent & Girard, Stéphane & Lekina, Alexandre, 2010. "Functional nonparametric estimation of conditional extreme quantiles," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 419-433, February.
    7. Abdelaati Daouia & Laurent Gardes & Stéphane Girard & Alexandre Lekina, 2011. "Kernel estimators of extreme level curves," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 311-333, August.
    8. Tong Siu Tung Wong & Wai Keung Li, 2015. "Extreme values identification in regression using a peaks-over-threshold approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(3), pages 566-576, March.
    9. Padoan, S.A. & Wand, M.P., 2008. "Mixed model-based additive models for sample extremes," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2850-2858, December.
    10. Chiara Bocci & Enrica Caporali & Alessandra Petrucci, 2013. "Geoadditive modeling for extreme rainfall data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(2), pages 181-193, April.
    11. Stan Tendijck & Philip Jonathan & David Randell & Jonathan Tawn, 2024. "Temporal evolution of the extreme excursions of multivariate k$$ k $$th order Markov processes with application to oceanographic data," Environmetrics, John Wiley & Sons, Ltd., vol. 35(3), May.
    12. 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.
    13. M. de Carvalho & K. F. Turkman & A. Rua, 2013. "Dynamic threshold modelling and the US business cycle," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(4), pages 535-550, August.
    14. Adam Butler & Janet E. Heffernan & Jonathan A. Tawn & Roger A. Flather, 2007. "Trend estimation in extremes of synthetic North Sea surges," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(4), pages 395-414, August.
    15. Zhang, Qingzhao & Li, Deyuan & Wang, Hansheng, 2013. "A note on tail dependence regression," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 163-172.
    16. Yaolan Ma & Bo Wei & Wei Huang, 2020. "A nonparametric estimator for the conditional tail index of Pareto-type distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(1), pages 17-44, January.
    17. Gardes, Laurent & Girard, Stéphane, 2008. "A moving window approach for nonparametric estimation of the conditional tail index," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2368-2388, November.
    18. Refk Selmi & Christos Kollias & Stephanos Papadamou & Rangan Gupta, 2017. "A Copula-Based Quantile-on-Quantile Regression Approach to Modeling Dependence Structure between Stock and Bond Returns: Evidence from Historical Data of India, South Africa, UK and US," Working Papers 201747, University of Pretoria, Department of Economics.
    19. António Rua & Miguel de Carvalho, 2010. "Nonstationary Extremes and the US Business Cycle," Working Papers w201003, Banco de Portugal, Economics and Research Department.
    20. Anne‐Laure Fougères & John P. Nolan & Holger Rootzén, 2009. "Models for Dependent Extremes Using Stable Mixtures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 42-59, March.

    More about this item

    Statistics

    Access and download statistics

    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:bla:jorssc:v:58:y:2009:i:1:p:25-45. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    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.