### Abstract

Language | English |
---|---|

Pages | 749-760 |

Number of pages | 12 |

Journal | Science China Mathematics |

Volume | 45 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jun 2002 |

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### Keywords

- ARCH
- bilinear model
- dependence
- tail probability

### Cite this

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*Science China Mathematics*, vol. 45, no. 6, pp. 749-760. https://doi.org/10.1360/02ys9082

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Tail dependence of random variables from ARCH and heavy-tailed Bilinear models

AU - Pan, Jiazhu

PY - 2002/6

Y1 - 2002/6

N2 - 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.

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.

KW - ARCH

KW - bilinear model

KW - dependence

KW - tail probability

U2 - 10.1360/02ys9082

DO - 10.1360/02ys9082

M3 - Article

VL - 45

SP - 749

EP - 760

JO - Science China Mathematics

T2 - Science China Mathematics

JF - Science China Mathematics

SN - 1674-7283

IS - 6

ER -