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Modelling non-stationary extremes with application to surface level ozone

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  • Emma F. Eastoe
  • Jonathan A. Tawn

Abstract

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. Copyright (c) 2009 Royal Statistical Society.

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.
  • Handle: RePEc:bla:jorssc:v:58:y:2009:i:1:p:25-45
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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9876.2008.00638.x
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    References listed on IDEAS

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    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.
    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.
    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.
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    1. repec:bla:jorssc:v:66:y:2017:i:5:p:941-962 is not listed on IDEAS
    2. Fernando Ferraz Nascimento & Dani Gamerman & Hedibert Freitas 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.
    3. 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.
    4. 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.
    5. 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.
    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.

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