### Abstract

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

Pages | 1169-1181 |

Number of pages | 12 |

Journal | Science China Mathematics |

Volume | 48 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2005 |

### Fingerprint

### Keywords

- tail probability
- stationary distribution
- nonlinear AR model
- heavy-tailed distribution
- statistics

### Cite this

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*Science China Mathematics*, vol. 48, no. 9, pp. 1169-1181. https://doi.org/10.1360/02ys0246

**On tail behaviour of nonlinear autoregressive functional conditional heteroscedastic model with heavy-tailed innovations.** / Pan, J.; Wu, G.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On tail behaviour of nonlinear autoregressive functional conditional heteroscedastic model with heavy-tailed innovations

AU - Pan, J.

AU - Wu, G.

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

KW - tail probability

KW - stationary distribution

KW - nonlinear AR model

KW - heavy-tailed distribution

KW - statistics

U2 - 10.1360/02ys0246

DO - 10.1360/02ys0246

M3 - Article

VL - 48

SP - 1169

EP - 1181

JO - Science China Mathematics

T2 - Science China Mathematics

JF - Science China Mathematics

SN - 1674-7283

IS - 9

ER -