Skip to main content
Springer Nature Link
Log in

Cluster Analysis of Time Series via Kendall Distribution

  • Chapter
Strengthening Links Between Data Analysis and Soft Computing

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 315))

Abstract

We present a method to cluster time series according to the calculation of the pairwise Kendall distribution function between them. A case study with environmental data illustrates the introduced methodology.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

eBook
USD 12.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Liao, T.W.: Clustering of time series data - a survey. Pattern Recogn. 38(11), 1857–1874 (2005)

    Article  MATH  Google Scholar 

  2. Embrechts, P., McNeil, A.J., Straumann, D.: Correlation and Dependence in Risk Management: Properties and Pitfalls. Cambridge Univ. Press, New York (2001)

    Google Scholar 

  3. Poulin, A., Huard, D., Favre, A.-C., Pugin, S.: Importance of tail dependence in bivariate frequency analysis. J. Hydrol. Eng. 12, 394–403 (2007)

    Article  Google Scholar 

  4. Gudendorf, G., Segers, J.: Extreme-value copulas. In: Jaworski, P., Durante, F., Härdle, W., Rychlik, T. (eds.) Copula Theory and its Applications. Lecture Notes in Statistics - Proceedings, vol. 198, pp. 127–145. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  5. Salvadori, G., De Michele, C., Kottegoda, N.T., Rosso, R.: Extremes in Nature. An Approach Using Copulas. Water Sci. and Technology Library 56. Springer (2007)

    Google Scholar 

  6. Jaworski, P.: Tail behaviour of copulas. In: Jaworski, P., Durante, F., Härdle, W., Rychlik, T. (eds.) Copula Theory and its Applications. Lecture Notes in Statistics - Proceedings, vol. 198, pp. 161–186. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  7. Gaetan, C., Grigoletto, M.: A hierarchical model for the analysis of spatial rainfall extremes. J. ABES 12(4), 434–449 (2007)

    MathSciNet  Google Scholar 

  8. Scotto, M.G., Barbosa, S.M., Alonso, A.M.: Extreme value and cluster analysis of European daily temperature series. Journal of Applied Statistics 38(12), 2793–2804 (2011)

    Article  MathSciNet  Google Scholar 

  9. Favre, A.-C., Adlouni, S.E., Perreault, L., Thiemonge, N., Bobee, B.: Multivariate hydrological frequency analysis using copulas. Water Resour. Res. 40 (2004)

    Google Scholar 

  10. Salvadori, G., De Michele, C.: Frequency analysis via copulas: theoretical aspects and applications to hydrological events. Water Resour. Res. 40 (2004)

    Google Scholar 

  11. Bárdossy, A.: Copula-based geostatistical models for groundwater quality parameters. Water Resour. Res. 42(11) (2006)

    Google Scholar 

  12. Bonazzi, A., Cusack, S., Mitas, C., Jewson, S.: The spatial structure of European wind storms as characterized by bivariate extreme-value Copulas. Nat. Hazards Earth Syst. Sci. 12, 1769–1782 (2012)

    Article  Google Scholar 

  13. Genest, C., Favre, A.-C.: Everything you always wanted to know about copula modeling but were afraid to ask. J. Hydrologic Eng. 12(4), 347–368 (2007)

    Article  Google Scholar 

  14. Durante, F., Pappadà, R., Torelli, N.: Clustering of financial time series in risky scenarios. Adv. Data Anal. Classif. (2013) (in press), doi: 10.1007/s11634-013-0160-4

    Google Scholar 

  15. De Luca, G., Zuccolotto, P.: A tail dependence-based dissimilarity measure for financial time series clustering. Adv. Data Anal. Classif. 5(4), 323–340 (2011)

    Article  MathSciNet  Google Scholar 

  16. Durante, F., Pappadà, R., Torelli, N.: Clustering of extreme observations via tail dependence estimation. Statist. Papers (in press, 2014)

    Google Scholar 

  17. Buishand, T., de Haan, L., Zhou, C.: On spatial extremes: With application to a rainfall problem. Ann. Appl. Statist. 2, 624–642 (2008)

    Article  MATH  Google Scholar 

  18. Cooley, D., Naveau, P., Poncet, P.: Variograms for spatial max-stable random fields. In: Dependence in Probability and Statistics. Lectures Notes in Statistics, pp. 373–390. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  19. Cooley, D., Nychka, D., Naveau, P.: Bayesian spatial modeling of extreme precipitation return levels. J. Amer. Statist. Assoc. 102, 824–840 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Robeson, S.M., Doty, J.A.: Identifying rogue air temperature stations using cluster analysis of percentile trends. J. Climate 18, 1275–1287 (2005)

    Article  Google Scholar 

  21. Scotto, M.G., Alonso, A.M., Barbosa, S.M.: Clustering time series of sea levels: Extreme value approach. J. Waterway, Port, Coastal, and Ocean Engrg. 136, 215–225 (2010)

    Article  Google Scholar 

  22. Salvadori, G., De Michele, C., Durante, F.: On the return period and design in a multivariate framework. Hydrol. Earth Syst. Sci. 15, 3293–3305 (2011)

    Article  Google Scholar 

  23. Salvadori, G., Durante, F., De Michele, C.: Multivariate return period calculation via survival functions. Water Resour. Res. 49(4), 2308–2311 (2013)

    Article  Google Scholar 

  24. Salvadori, G., Durante, F., Perrone, E.: Semi–parametric approximation of the Kendall’s distribution and multivariate return periods. J. SFdS 154(1), 151–173 (2013)

    MathSciNet  Google Scholar 

  25. Genest, C., Rivest, L.-P.: Statistical inference procedures for bivariate Archimedean copulas. J. Amer. Statist. Assoc. 88(423), 1034–1043 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  26. Genest, C., Rivest, L.-P.: On the multivariate probability integral transformation. Statist. Probab. Lett. 53(4), 391–399 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  27. Capéraà, P., Fougères, A.-L., Genest, C.: A stochastic ordering based on a decomposition of Kendall’s tau. In: Beneš, V., Štěpán, J (Eds.) Distributions with Given Marginals and Moment Problems. Kluwer Academic Publishers, Dordrecht, pp. 81–86

    Google Scholar 

  28. Nelsen, R.B., Quesada–Molina, J.J., Rodríguez–Lallena, J.A., Úbeda–Flores, M.: Kendall distribution functions. Statist. Probab. Lett. 65, 263–268 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  29. Genest, C., Nešlehová, G., Ziegel, J., Inference, J.: in multivariate Archimedean copula models. TEST 20, 223–256 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  30. Barbe, P., Genest, C., Ghoudi, K., Rémillard, B.: On Kendall’s process. J. Multivar. Anal. 58(1996), 197–229 (1996)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Economics and Management, Free University of Bozen–Bolzano, Bolzano, Italy

    Fabrizio Durante & Roberta Pappadà

Authors
  1. Fabrizio Durante
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roberta Pappadà
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fabrizio Durante .

Editor information

Editors and Affiliations

  1. Polish Academy of Sciences, Faculty of Mathematics and Information Sciences, Systems Research Institute and Warsaw University of Technology, Warsaw, Poland

    Przemyslaw Grzegorzewski

  2. Polish Academy of Sciences, Faculty of Mathematics and Information Sciences, Systems Research Institute and Warsaw University of Technology, Warsaw, Poland

    Marek Gagolewski

  3. Polish Academy of Sciences Systems Research Institute, Warsaw, Poland

    Olgierd Hryniewicz

  4. Departamento de Estadistica e I.O. y D.M., University of Oviedo, Oviedo, Spain

    María Ángeles Gil

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Durante, F., Pappadà, R. (2015). Cluster Analysis of Time Series via Kendall Distribution. In: Grzegorzewski, P., Gagolewski, M., Hryniewicz, O., Gil, M. (eds) Strengthening Links Between Data Analysis and Soft Computing. Advances in Intelligent Systems and Computing, vol 315. Springer, Cham. https://doi.org/10.1007/978-3-319-10765-3_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-10765-3_25

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10764-6

  • Online ISBN: 978-3-319-10765-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics