Skip to main content
SpringerLink
Log in

Rare-event asymptotics for the number of exceedances of multiplicative factor models

  • Published:
Extremes Aims and scope Submit manuscript

Abstract

In this paper, we study the asymptotic distribution of the number of exceedances of multiplicative factor models under the rare-event condition that the probability the number of exceedances is positive tends to zero. We show that the asymptotic conditional distribution (given that there is at least one exceedance), as well as the condition such that the probability of the conditional event tends to zero, depend on the distribution of the multiplicative disturbances. When the distribution of the disturbances is not a heavy-tailed distribution, it is necessary to normalize the number of exceedances to get a non-degenerate asymptotic distribution.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bingham, N.H., Goldie, C.M., Teugels, J.L.: Regular Variation. Cambridge University Press, Cambridge (1987)

    Book  MATH  Google Scholar 

  • Davis, R.A., Mikosch, T.: Limit theory for the sample ACF of stationary process with heavy tails with applications to ARCH. Ann. Statist. 26, 2049–2080 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  • Embrechts, P., Klüppelberg, C., Mikosch, T.: Modelling Extremal Events. Springer, Berlin (1997)

    Book  MATH  Google Scholar 

  • Falk, M., Hüsler, J., Reiss, R.D.: Laws of Small Numbers: Extremes and Rare Events, 3rd edn. Birkhauser (2011)

  • de Haan, L., Resnick, S., Rootzen, H., de Vries, C.G.: Extremal behaviour of solutions to a stochastic difference equation with application to ARCH processes. Stochastic Process. Appl. 32, 213–224 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  • Leadbetter, M.R.: On extreme values in stationary sequences. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 28, 289–303 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  • Leadbetter, M.R., Lindgren, G., Rootzen, H.: Extremes and Related Properties of Random Sequences and Processes. Springer, New York (1983)

    Book  MATH  Google Scholar 

  • Perfekt, R.: Extremal behaviour of stationary Markov chains with applications. Ann. Appl. Probab. 4, 529–548 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  • Resnick, S.I.: Extreme Values Regular Variation and Point Processes. Springer, New-York (1987)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université de Lyon, Université Lyon 1, Institut de Science Financière et d’Assurances, 50 Avenue Tony Garnier, 69007, Lyon, France

    Christian Y. Robert

Authors
  1. Christian Y. Robert
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christian Y. Robert.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Robert, C.Y. Rare-event asymptotics for the number of exceedances of multiplicative factor models. Extremes 18, 511–527 (2015). https://doi.org/10.1007/s10687-015-0222-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10687-015-0222-4

Keywords

AMS 2000 Subject Classifications

Search

Navigation