Tail dependence of random variables from ARCH and heavy-tailed bilinear models |
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Authors: | Jiazhu Pan |
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Institution: | Department of Financial Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871,China |
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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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Keywords: | ARCH bilinear model dependence tail probability |
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