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

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.
LanguageEnglish
Pages749-760
Number of pages12
JournalScience China Mathematics
Volume45
Issue number6
DOIs
Publication statusPublished - Jun 2002

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Tail Dependence
Bilinear Model
Random variable
First-order
Stationary Time Series
Nonlinear Time Series
Conditional probability
Finance
Explicit Formula
Tail
Dependent
Model
Class
Tail dependence
Random variables
Innovation
Meaning

Keywords

  • ARCH
  • bilinear model
  • dependence
  • tail probability

Cite this

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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.",
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Tail dependence of random variables from ARCH and heavy-tailed Bilinear models. / Pan, Jiazhu.

In: Science China Mathematics, Vol. 45, No. 6, 06.2002, p. 749-760.

Research output: Contribution to journalArticle

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AB - 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.

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