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

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• 作者：Christian Y. Robert
• 关键词：Multiplicative factor models ; Number of exceedances ; Asymptotic conditional distributions ; 60G70 ; 60F99
• 刊名：Extremes
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：18
• 期：3
• 页码：511-527
• 全文大小：279 KB
• 参考文献：Bingham, N.H., Goldie, C.M., Teugels, J.L.: Regular Variation. Cambridge University Press, Cambridge (1987)View Article
  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鈥?080 (1998)MathSciNet View Article
  Embrechts, P., Kl眉ppelberg, C., Mikosch, T.: Modelling Extremal Events. Springer, Berlin (1997)View Article
  Falk, M., H眉sler, 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鈥?24 (1989)MathSciNet View Article
  Leadbetter, M.R.: On extreme values in stationary sequences. Zeitschrift f眉r Wahrscheinlichkeitstheorie und Verwandte Gebiete 28, 289鈥?03 (1974)MathSciNet View Article
  Leadbetter, M.R., Lindgren, G., Rootzen, H.: Extremes and Related Properties of Random Sequences and Processes. Springer, New York (1983)View Article
  Perfekt, R.: Extremal behaviour of stationary Markov chains with applications. Ann. Appl. Probab. 4, 529鈥?48 (1994)MathSciNet View Article
  Resnick, S.I.: Extreme Values Regular Variation and Point Processes. Springer, New-York (1987)View Article
  
• 作者单位：Christian Y. Robert (1)
  
  1. Universit茅 de Lyon, Universit茅 Lyon 1, Institut de Science Financi猫re et d鈥橝ssurances, 50 Avenue Tony Garnier, 69007, Lyon, France
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics
  Quality Control, Reliability, Safety and Risk
  Civil Engineering
  Hydrogeology
  Environmental Management
  Statistics for Business, Economics, Mathematical Finance and Insurance
  
• 出版者：Springer U.S.
• ISSN：1572-915X

文摘

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.