“But he does not wear any clothes” said the little child in Hans Christian Andersen’s “The Emperor’s New Clothes.”
Similar content being viewed by others
References
Basrak, B., Davis, R.A., Mikosch, T.: Regular variation of GARCH processes. Stoch. Process. Appl. 99, 95–116 (2002)
Brockwell, P.J., Davis, R.A.: Time Series: Theory and Methods. 2nd edn. Springer, Berlin Heidelberg New York (1991)
Brockwell, P.J., Davis, R.A.: Introduction to Time Series and Forecasting. Springer, Berlin Heidelberg New York (1996)
Carmona, R.A.: Statistical Analysis of Financial Data in S-PLUS. Springer, Berlin Heidelberg New York (2004)
Embrechts, P., Klüppelberg, C., Mikosch, T.: Modelling Extremal Events for Insurance and Finance. Springer, Berlin Heidelberg New York (1997)
Embrechts, P., McNeil, A., Straumann, D.: Correlation and dependence in risk management: Properties and pitfalls. In: Dempster, M.A.H. (ed.) Risk Management: Value at Risk and Beyond, pp. 176–223. Cambridge University Press, UK (2002)
Glasserman, P.: Monte-Carlo Methods in Financial Engineering. Springer, Berlin Heidelberg New York (2004)
Galambos, J.: Asymptotic Theory of Extreme Order Statistics. 2nd edn. Krieger, Malabar, Florida (1987)
Genest, C., Rivest, L.-P.: Statistical inference procedures for bivariate Archimedean copulas. J. Am. Stat. Assoc. 88, 1034–1043 (1993)
de Haan, L., Resnick, S.I.: Estimating the limit distribution of multivariate extremes. Stoch. Models 9, 275–309 (1993)
de Haan, L., de Ronde, J.: Sea and wind: multivariate extremes at work. Extremes 1, 7–45 (1998)
Heffernan, J., Resnick, S.: Hidden regular variation and the rank transform. Adv. Appl. Probab. 37, 393–414 (2005)
Hult, H., Lindskog, F.: Extremal behavior of regularly varying stochastic processes. Stoch. Process. Appl. 115, 249–274 (2005)
The International Actuarial Association: A global framework for insurer solvency assessment. Research Report. www.actuaries.org (2004)
Kotz, S., Nadarajah, S.: Extreme Value Distributions: Theory and Applications. Imperial College Press, London (2000)
Maulik, K., Resnick, S.: Characterizations and examples of hidden regular variation. Technical Report. www.orie.cornell.edu/~sid/ (2004)
McNeil, A., Frey, R., Embrechts, P.: Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton University Press, New Jersey (2005)
Mikosch, T.: Modeling dependence and tails of financial time series. In: Finkenstädt, B., Rootzén, H. (eds.) Extreme Values in Finance, Telecommunications, and the Environment, pp. 187–286. Chapman & Hall, Boca Raton (2003)
Mikosch, T.: How to model multivariate extremes if one must? Stat. Neerl. 59, 324–338 (2005)
Mikosch, T., Samorodnitsky, G.: The supremum of a negative drift random walk with dependent heavy-tailed steps. Ann. Appl. Probab. 10, 1025–1064 (2000)
Nelsen, R.B.: An Introduction to Copulas. Lecture Science in Statistic vol. 1389, Springer, Berlin Heidelberg New York (1999)
Einmahl, J.H.J., de Haan, L., Piterbarg, V.I.: Nonparametric estimation of the spectral (Unsupported LaTeX command \ms) of an (Unsupported LaTeX command \evd) . Ann. Stat. 29, 1401–1423 (2001)
Resnick, S.I.: Point processes, regular variation and weak convergence. Adv. Appl. Probab. 18, 66–138 (1986)
Resnick, S.I.: Extreme Values, Regular Variation, and Point Processes. Springer, Berlin Heidelberg New York (1987)
Resnick, S.I.: On the foundations of multivariate heavy-tail analysis. Stochastic methods and their applications. J. Appl. Probab. 41A, 191–212 (2004)
Song, P., Fan, Y., Kalbfleisch, J.D.: Maximization by parts in likelihood inference. Technical Report, Vanderbilt University. http://econpapers.repec.org/paper/vanwpaper/0319.htm> (2003)
Zolotarev, V.: Modern Theory of Summation of Random Variables. VSP, Utrecht (1997)
Author information
Authors and Affiliations
Corresponding author
Additional information
Mikosch’s research is partially supported by the Danish Research Council (SNF) GrantNo 21-04-0400. This is a discussion paper which was initiated at the 4th InternationalConference on Extreme Value Analysis in Gothenburg, 15–19 August, 2005; seehttp://www.math.ku.dk/~mikosch/maphysto_extremes_2005/extremes.
Rights and permissions
About this article
Cite this article
Mikosch, T. Copulas: Tales and facts. Extremes 9, 3–20 (2006). https://doi.org/10.1007/s10687-006-0015-x
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10687-006-0015-x