Tail dependence of random variables from ARCH and heavy-tailed Bilinear models

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Abstract

Discussed in this paper is the dependent structure in the tails of distributions of random variables from some heavy-tailed stationary nonlinear time series. One class of models discussed is the first-order autoregressive conditional heteroscedastic (ARCH) process introduced by Engle (1982). The other class is the simple first-order bilinear models driven by heavy-tailed innovations. We give some explicit formulas for the asymptotic values of conditional probabilities used for measuring the tail dependence between two random variables from these models. Our results have significant meanings in finance.
Original languageEnglish
Pages (from-to)749-760
Number of pages12
JournalScience China Mathematics
Volume45
Issue number6
DOIs
Publication statusPublished - Jun 2002

Keywords

  • ARCH
  • bilinear model
  • dependence
  • tail probability

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