The Annals of Applied Statistics

Ground-level ozone: Evidence of increasing serial dependence in the extremes

Debbie J. Dupuis and Luca Trapin

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As exposure to successive episodes of high ground-level ozone concentrations can result in larger changes in respiratory function than occasional exposure buffered by lengthy recovery periods, the analysis of extreme values in a series of ozone concentrations requires careful consideration of not only the levels of the extremes but also of any dependence appearing in the extremes of the series. Increased dependence represents increased health risks and it is thus important to detect any changes in the temporal dependence of extreme values. In this paper we establish the first test for a change point in the extremal dependence of a stationary time series. The test is flexible, easy to use and can be extended along several lines. The asymptotic distributions of our estimators and our test are established. A large simulation study verifies the good finite sample properties. The test allows us to show that there has been a significant increase in the serial dependence of the extreme levels of ground-level ozone concentrations in Bloomsbury (UK) in recent years.

Article information

Ann. Appl. Stat., Volume 13, Number 1 (2019), 34-59.

Received: February 2018
Revised: May 2018
First available in Project Euclid: 10 April 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Threshold exceedances hierarchical models trawl process change point


Dupuis, Debbie J.; Trapin, Luca. Ground-level ozone: Evidence of increasing serial dependence in the extremes. Ann. Appl. Stat. 13 (2019), no. 1, 34--59. doi:10.1214/18-AOAS1183.

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  • Ackermann, R., Hughes, G., Hanrahan, D., Somani, A., Aggarwal, S., Fitzgerald, A., Dixon, J., Kunte, A., Lovei, M. and Lvovsky, K. (1999). Pollution Prevention and Abatement Handbook 1998: Toward Cleaner Production. World Bank Group, Washington, DC. Available at
  • Air Quality Expert Group (2009). Ozone in the United Kingdom. Available at
  • Andrews, D. W. K. (1993). Tests for parameter instability and structural change with unknown change point. Econometrica 61 821–856.
  • Bai, J. and Perron, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica 66 47–78.
  • Barndorff-Nielsen, O. E., Benth, F. E. and Veraart, A. E. D. (2011). Ambit processes and stochastic partial differential equations. In Advanced Mathematical Methods for Finance 35–74. Springer, Heidelberg.
  • Bortot, P. and Gaetan, C. (2014). A latent process model for temporal extremes. Scand. J. Stat. 41 606–621.
  • Bortot, P. and Gaetan, C. (2016). Latent process modelling of threshold exceedances in hourly rainfall series. J. Agric. Biol. Environ. Stat. 21 531–547.
  • Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer Series in Statistics. Springer, London.
  • Cox, D. R. and Reid, N. (2004). A note on pseudolikelihood constructed from marginal densities. Biometrika 91 729–737.
  • Davis, R. A. and Mikosch, T. (2009). The extremogram: A correlogram for extreme events. Bernoulli 15 977–1009.
  • Davis, R. A. and Yau, C. Y. (2011). Comments on pairwise likelihood in time series models. Statist. Sinica 21 255–277.
  • Dierckx, G. and Teugels, J. L. (2010). Change point analysis of extreme values. Environmetrics 21 661–686.
  • Dupuis, D. J. (2005). Ozone concentrations: A robust analysis of multivariate extremes. Technometrics 47 191–201.
  • Dupuis, D. J. (2012). Modeling waves of extreme temperature: The changing tails of four cities. J. Amer. Statist. Assoc. 107 24–39.
  • Dupuis, D. J., Sun, Y. and Wang, H. J. (2015). Detecting change-points in extremes. Stat. Interface 8 19–31.
  • Eastoe, E. F. and Tawn, J. A. (2009). Modelling non-stationary extremes with application to surface level ozone. J. R. Stat. Soc. Ser. C. Appl. Stat. 58 25–45.
  • Environmental Research Group, King’s College London (2015). London Air Quality Network Database. King’s College, London. Available at
  • Ferro, C. A. T. and Segers, J. (2003). Inference for clusters of extreme values. J. R. Stat. Soc. Ser. B. Stat. Methodol. 65 545–556.
  • Fiore, A. M., Naik, V., Spracklen, D. V., Steiner, A., Unger, N., Prather, M., Bergmann, D., Cameron-Smith, P. J., Cionni, I. et al. (2012). Global air quality and climate. Chem. Soc. Rev. 41 6663–6683.
  • Gilleland, E. and Katz, R. W. (2016). extRemes 2.0: An extreme value analysis package in R. J. Stat. Softw. 72 1–39.
  • Huser, R. and Davison, A. C. (2014). Space-time modelling of extreme events. J. R. Stat. Soc. Ser. B. Stat. Methodol. 76 439–461.
  • Jacob, D. J. and Winner, D. A. (2009). Effect of climate change on air quality. Atmos. Environ. 43 51–63.
  • Kim, M. and Lee, S. (2009). Test for tail index change in stationary time series with Pareto-type marginal distribution. Bernoulli 15 325–356.
  • Leadbetter, M. R. (1983). Extremes and local dependence in stationary sequences. Z. Wahrsch. Verw. Gebiete 65 291–306.
  • Ledford, A. W. and Tawn, J. A. (2003). Diagnostics for dependence within time series extremes. J. R. Stat. Soc. Ser. B. Stat. Methodol. 65 521–543.
  • Newey, W. K. and McFadden, D. (1994). Large sample estimation and hypothesis testing. In Handbook of Econometrics, Vol. IV. Handbooks in Econom. 2 2111–2245. North-Holland, Amsterdam.
  • Newey, W. K. and West, K. D. (1987). A simple, positive semidefinite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55 703–708.
  • Noven, R. C., Veraart, A. E. and Gandy, A. (2015a). A latent trawl process model for extreme values. Available at
  • Noven, R. C., Veraart, A. E. and Gandy, A. (2017b). A latent trawl process model for extreme values. Available at
  • Pickands, J. III (1975). Statistical inference using extreme order statistics. Ann. Statist. 3 119–131.
  • Pope, R. J. et al. (2016). The impact of synoptic weather on UK surface ozone and implications for premature mortality. Environ. Res. Lett. 11 124004.
  • Quintos, C., Fan, Z. and Phillips, P. C. B. (2001). Structural change tests in tail behaviour and the Asian crisis. Rev. Econ. Stud. 68 633–663.
  • Schell, J. L. and Prather, M. J. (2017). Co-occurrence of extremes in surface ozone, particulate matter, and temperature over eastern North America. Proc. Natl. Acad. Sci. USA 114 2854–2859.
  • Shen, L., Mickley, L. J. and Gilleland, E. (2016). Impact of increasing heat waves on US ozone episodes in the 2050s: Results from a multimodel analysis using extreme value theory. Geophys. Res. Lett. 43 4017–4025.
  • Shephard, N. and Yang, J. J. (2017). Continuous time analysis of fleeting discrete price moves. J. Amer. Statist. Assoc. 112 1090–1106.
  • Smith, R. L. (1985). Maximum likelihood estimation in a class of nonregular cases. Biometrika 72 67–90.
  • Smith, R. L. (1989). Extreme value analysis of environmental time series: An application to trend detection in ground-level ozone. Statist. Sci. 4 367–393.
  • WHO (World Health Organization) (1987). Air Quality Guidelines for Europe. WHO Regional Office for Europe, Copenhagen.
  • WHO (World Health Organization) (2000). Air Quality Guidelines for Europe, Second ed. WHO Regional Office for Europe, Copenhagen.
  • Wolpert, R. L. and Ickstadt, K. (1998). Poisson/gamma random field models for spatial statistics. Biometrika 85 251–267.