IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v199y2024ics0167947324001099.html
   My bibliography  Save this article

Modelling non-stationarity in asymptotically independent extremes

Author

Listed:
  • Murphy-Barltrop, C.J.R.
  • Wadsworth, J.L.

Abstract

In many practical applications, evaluating the joint impact of combinations of environmental variables is important for risk management and structural design analysis. When such variables are considered simultaneously, non-stationarity can exist within both the marginal distributions and dependence structure, resulting in complex data structures. In the context of extremes, few methods have been proposed for modelling trends in extremal dependence, even though capturing this feature is important for quantifying joint impact. Moreover, most proposed techniques are only applicable to data structures exhibiting asymptotic dependence. Motivated by observed dependence trends of data from the UK Climate Projections, a novel semi-parametric modelling framework for bivariate extremal dependence structures is proposed. This framework can capture a wide variety of dependence trends for data exhibiting asymptotic independence. When applied to the climate projection dataset, the model detects significant dependence trends in observations and, in combination with models for marginal non-stationarity, can be used to produce estimates of bivariate risk measures at future time points.

Suggested Citation

  • Murphy-Barltrop, C.J.R. & Wadsworth, J.L., 2024. "Modelling non-stationarity in asymptotically independent extremes," Computational Statistics & Data Analysis, Elsevier, vol. 199(C).
    • Handle: RePEc:eee:csdana:v:199:y:2024:i:c:s0167947324001099
    DOI: 10.1016/j.csda.2024.108025
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947324001099
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2024.108025?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. 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. 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.
    3. Marcon, Giulia & Padoan, Simone & Naveau, Philippe & Muliere, Pietro & Segers, Johan, 2017. "Multivariate nonparametric estimation of the Pickands dependence function using Bernstein polynomials," LIDAM Reprints ISBA 2017003, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. 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.
    5. 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.
    6. 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.
    7. J. L. Wadsworth & J. A. Tawn & A. C. Davison & D. M. Elton, 2017. "Modelling across extremal dependence classes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 149-175, January.
    8. Mhalla, Linda & Chavez-Demoulin, Valérie & Naveau, Philippe, 2017. "Non-linear models for extremal dependence," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 49-66.
    9. Frahm, Gabriel, 2006. "On the extremal dependence coefficient of multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1470-1481, August.
    10. Benjamin D. Youngman, 2019. "Generalized Additive Models for Exceedances of High Thresholds With an Application to Return Level Estimation for U.S. Wind Gusts," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1865-1879, October.
    11. Laurens de Haan & Chen Zhou, 2021. "Trends in Extreme Value Indices," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(535), pages 1265-1279, July.
    12. 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.
    13. Raphaël Huser & Jennifer L. Wadsworth, 2019. "Modeling Spatial Processes with Unknown Extremal Dependence Class," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 434-444, January.
    14. Stuart Coles, 2002. "Models and inference for uncertainty in extremal dependence," Biometrika, Biometrika Trust, vol. 89(1), pages 183-196, March.
    15. 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.
    16. S. Caires & J. Ferreira, 2005. "On the Non-parametric Prediction of Conditionally Stationary Sequences," Statistical Inference for Stochastic Processes, Springer, vol. 8(2), pages 151-184, September.
    17. Miguel de Carvalho & Anthony C. Davison, 2014. "Spectral Density Ratio Models for Multivariate Extremes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 764-776, June.
    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. 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.
    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. R. Shooter & E. Ross & A. Ribal & I. R. Young & P. Jonathan, 2021. "Spatial dependence of extreme seas in the North East Atlantic from satellite altimeter measurements," Environmetrics, John Wiley & Sons, Ltd., vol. 32(4), June.
    4. Mhalla, Linda & Chavez-Demoulin, Valérie & Naveau, Philippe, 2017. "Non-linear models for extremal dependence," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 49-66.
    5. de Valk, Cees, 2016. "A large deviations approach to the statistics of extreme events," Other publications TiSEM 117b3ba0-0e40-4277-b25e-d, Tilburg University, School of Economics and Management.
    6. Richards, Jordan & Tawn, Jonathan A., 2022. "On the tail behaviour of aggregated random variables," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    7. 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.
    8. Liu, Y. & Tawn, J.A., 2014. "Self-consistent estimation of conditional multivariate extreme value distributions," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 19-35.
    9. Guillou, Armelle & Padoan, Simone A. & Rizzelli, Stefano, 2018. "Inference for asymptotically independent samples of extremes," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 114-135.
    10. 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.
    11. Jordan Richards & Jennifer L. Wadsworth, 2021. "Spatial deformation for nonstationary extremal dependence," Environmetrics, John Wiley & Sons, Ltd., vol. 32(5), August.
    12. Papastathopoulos, Ioannis & Tawn, Jonathan A., 2016. "Conditioned limit laws for inverted max-stable processes," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 214-228.
    13. Daniel Maposa & Anna M. Seimela & Caston Sigauke & James J. Cochran, 2021. "Modelling temperature extremes in the Limpopo province: bivariate time-varying threshold excess approach," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 107(3), pages 2227-2246, July.
    14. Alexandra Ramos & Anthony Ledford, 2009. "A new class of models for bivariate joint tails," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 219-241, January.
    15. Kresning, Boma & Hashemi, M. Reza & Shirvani, Amin & Hashemi, Javad, 2024. "Uncertainty of extreme wind and wave loads for marine renewable energy farms in hurricane-prone regions," Renewable Energy, Elsevier, vol. 220(C).
    16. 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.
    17. Marmai, Nadin & Franco Villoria, Maria & Guerzoni, Marco, 2016. "How the Black Swan damages the harvest: statistical modelling of extreme events in weather and crop production in Africa, Asia, and Latin America," Department of Economics and Statistics Cognetti de Martiis LEI & BRICK - Laboratory of Economics of Innovation "Franco Momigliano", Bureau of Research in Innovation, Complexity and Knowledge, Collegio 201605, University of Turin.
    18. 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.
    19. Kereszturi, Mónika & Tawn, Jonathan, 2017. "Properties of extremal dependence models built on bivariate max-linearity," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 52-71.
    20. Simpson, Emma S. & Wadsworth, Jennifer L. & Tawn, Jonathan A., 2021. "A geometric investigation into the tail dependence of vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 184(C).

    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:csdana:v:199:y:2024:i:c:s0167947324001099. 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/locate/csda .

    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.