Skip to main content
SpringerLink
Log in

Time Series Procedures to Improve Extreme Quantile Estimation

  • Conference paper
  • First Online:
Statistical Modelling and Risk Analysis (ICRA 2022)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 430))

Included in the following conference series:

Abstract

Although extreme events can occur rarely, they may have significant social and economic impacts. To assess the risk of extreme events, it is important to study the extreme quantiles of the distribution. The accurate semi-parametric estimation of high quantiles depends strongly on the estimation of some crucial parameters that appear in extreme value theory. Procedures that combine extreme value theory and time series modelling have revealed themselves as a nice compromise to capture extreme events. Here we study the estimation of extreme quantiles after adequate time series modelling. Using the R software, our approach will be applied to the daily mean flow discharge rate values of two rivers in Portugal.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    From [18].

  2. 2.

    Download from “http://snirh.apambiente.pt at 14/07/2022.”

References

  1. Chavez-Demoulin, V., Davison, A.C.: Modelling time series extremes. REVSTAT Stat. J. 10(1), 109–133 (2012)

    MathSciNet  MATH  Google Scholar 

  2. Rydell, S.: The use of extreme value theory and time series analysis to estimate risk measures for extreme events. Master’s thesis, Umeå University, Umeå (2013)

    Google Scholar 

  3. Neves, M.M., Cordeiro, C.: Modelling (and forecasting) extremes in time series: a naive approach. In: Atas do XXXIII Congresso da Sociedade Portuguesa de Estatística, Lisboa, 18–21 Outubro 2017, pp. 189–202 (2020)

    Google Scholar 

  4. Yozgatlıgil, C., Türkeş, M.: Extreme value analysis and forecasting of maximum precipitation amounts in the western Black Sea subregion of Turkey. Int. J. Climatol. 38(15), 5447–5458 (2018)

    Article  Google Scholar 

  5. R Core Team. R: A language and environment for statistical computing. R Found. for Statistical Computing, Vienna (2022). https://www.R-project.org/

  6. Gumbel, E.J.: Statistics of Extremes. Columbia University Press, New York (1958, 2004)

    Google Scholar 

  7. Fréchet, M.: Sur la loi de probabilité de l’écart maximum. Ann. Soc. Polon. Math. (Cracovie) 6, 93–116 (1927)

    Google Scholar 

  8. Fisher, R.A., Tippett, L.H.C.: Limiting forms of the frequency distributions of the largest or smallest member of a sample. Proc. Camb. Philos. Soc. 24, 180–190 (1928)

    Article  MATH  Google Scholar 

  9. Gumbel, E.J.: Les valeurs extrêmes des distributions statistiques. Ann. Inst. Henri Poincaré, 5(2), 115–158 (1935)

    MathSciNet  MATH  Google Scholar 

  10. von Mises, R.: La distribution de la plus grande de n valeurs. American Mathematical Society, Reprinted in Selected Papers Volumen II, Providence (1954), pp. 271–294 (1936)

    MATH  Google Scholar 

  11. Gnedenko, B.V.: Sur la distribution limite d’une série aléatoire. Ann. Math. 44, 423–453 (1943)

    Article  MathSciNet  MATH  Google Scholar 

  12. de Haan, L.: On Regular Variation and Its Applications to the Weak Convergence of Sample Extremes. Mathematical Centre Tract 32. D. Reidel, Amsterdam, Dordrecht (1970)

    Google Scholar 

  13. Hill, B.M.: A simple general approach to inference about the tail of a distribution. Ann. Stat. 3, 1163–1174 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  14. Caeiro, F., Gomes, M.I., Pestana, D.D.: Direct reduction of bias of the classical Hill estimator. Revstat 3, 111–136 (2005)

    MathSciNet  MATH  Google Scholar 

  15. Fraga, A., Gomes, M.I., Laurens, de H.: A new class of semi-parametric estimators of the second order parameter. Port. Math. 60(2), 193–214 (2003)

    MathSciNet  MATH  Google Scholar 

  16. Gomes, M.I., Martins, M.J.: “Asymptotically unbiased” estimators of the tail index based on external estimation of the second order parameter. Extremes 5, 5–31 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  17. Weissman, I.: Estimation of parameters and large quantiles based on the k largest observations. J. Am. Stat. Assoc. 73, 812–815 (1978)

    MathSciNet  MATH  Google Scholar 

  18. DeLurgio, S.A.: Forescasting Principles and Applications. McGraw-Hill International Editions, Boston (1998)

    Google Scholar 

  19. Hyndman, R.J., Athanasopoulos, G.: Forecasting: Principles and Practice, 2nd edn. OTexts, Melbourne (2018). Accessed 4th July 2022. http://OTexts.com/fpp2

Download references

Acknowledgements

Manuela Neves and Clara Cordeiro are partially financed by national funds through FCT – Fundação para a Ciência e a Tecnologia under the project UIDB/00006/2020. Dora Prata Gomes is financed by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications).

Author information

Authors and Affiliations

  1. Faculdade de Ciências e Tecnologia, Universidade do Algarve, Faro, Portugal

    Clara Cordeiro

  2. CEAUL – Centro de Estatística e Aplicações, Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal

    Clara Cordeiro

  3. Center for Mathematics and Applications (NOVA Math) and Department of Mathematics, NOVA FCT, Caparica, Portugal

    Dora P. Gomes

  4. Instituto Superior de Agronomia, Lisboa, Portugal

    M. Manuela Neves

  5. CEAUL – Centro de Estatística e Aplicações, Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal

    M. Manuela Neves

Authors
  1. Clara Cordeiro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dora P. Gomes
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Manuela Neves
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Clara Cordeiro .

Editor information

Editors and Affiliations

  1. Univeristy of West Attica, Egaleo, Greece

    Christos P. Kitsos

  2. Universidade Aberta, Lisboa, Portugal

    Teresa A. Oliveira

  3. University of Perugia, Perugia, Italy

    Francesca Pierri

  4. University of Salerno, Fisciano, Italy

    Marialuisa Restaino

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Cordeiro, C., Gomes, D.P., Neves, M.M. (2023). Time Series Procedures to Improve Extreme Quantile Estimation. In: Kitsos, C.P., Oliveira, T.A., Pierri, F., Restaino, M. (eds) Statistical Modelling and Risk Analysis. ICRA 2022. Springer Proceedings in Mathematics & Statistics, vol 430. Springer, Cham. https://doi.org/10.1007/978-3-031-39864-3_6

Download citation

Publish with us

Policies and ethics

Search

Navigation