Functional weak convergence of partial maxima processes

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• 作者：Danijel Krizmanić
• 关键词：Extremal index ; Functional limit theorem ; Regular variation ; Skorohod J 1 topology ; Strong mixing ; Weak convergence ; 60F17 ; 60G52 ; 60G70
• 刊名：Extremes
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：19
• 期：1
• 页码：7-23
• 全文大小：280 KB
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• 作者单位：Danijel Krizmanić (1)
  
  1. University of Rijeka, Radmile Matejčić 2, 51000, Rijeka, Croatia
  
• 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

For a strictly stationary sequence of nonnegative regularly varying random variables (X _n ) we study functional weak convergence of partial maxima processes \(M_{n}(t) = \bigvee _{i=1}^{\lfloor nt \rfloor }X_{i},\,t \in [0,1]\) in the space D[0, 1] with the Skorohod J ₁ topology. Under the strong mixing condition, we give sufficient conditions for such convergence when clustering of large values do not occur. We apply this result to stochastic volatility processes. Further we give conditions under which the regular variation property is a necessary condition for J ₁ and M ₁ functional convergences in the case of weak dependence. We also prove that strong mixing implies the so-called Condition \(\mathcal {A}(a_{n})\) with the time component. Keywords Extremal index Functional limit theorem Regular variation Skorohod J ₁ topology Strong mixing Weak convergence