Pan, J. and Wu, G.
(2005)
*On tail behaviour of nonlinear autoregressive functional conditional heteroscedastic model with heavy-tailed innovations.*
Science in China Series A: Mathematics, 48 (9).
pp. 1169-1181.
ISSN 1006-9283

## Abstract

We study the tail probability of the stationary distribution of nonparametric nonlinear autoregressive functional conditional heteroscedastic (NARFCH) model with heavy-tailed innovations. Our result shows that the tail of the stationary marginal distribution of an NARFCH series is heavily dependent on its conditional variance. When the innovations are heavy-tailed, the tail of the stationary marginal distribution of the series will become heavier or thinner than that of its innovations. We give some specific formulas to show how the increment or decrement of tail heaviness depends on the assumption on the conditional variance function. Some examples are given.

Item type: | Article |
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ID code: | 4932 |

Keywords: | tail probability, stationary distribution, nonlinear AR model, heavy-tailed distribution, statistics, Probabilities. Mathematical statistics, Mathematics(all) |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Strathprints Administrator |

Date Deposited: | 30 Nov 2007 |

Last modified: | 10 Dec 2015 17:11 |

URI: | http://strathprints.strath.ac.uk/id/eprint/4932 |

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