### Abstract

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

Pages | 321-338 |

Number of pages | 18 |

Journal | Science China Mathematics |

Volume | 47 |

Issue number | 3 |

DOIs | |

Publication status | Published - May 2004 |

### Fingerprint

### Keywords

- risk analysis
- infinite weighted sum
- moving average
- bilinear model
- stochastic difference equation
- tail probability
- vague convergence

### Cite this

*Science China Mathematics*,

*47*(3), 321-338. https://doi.org/10.1360/02ys0317

}

*Science China Mathematics*, vol. 47, no. 3, pp. 321-338. https://doi.org/10.1360/02ys0317

**How does innovation tail risk determine marginal tail risk of a stationary financial time series?** / Pan, Jiazhu; Yu, Bosco W. T.; Pang, W. K.

Research output: Contribution to journal › Article

TY - JOUR

T1 - How does innovation tail risk determine marginal tail risk of a stationary financial time series?

AU - Pan, Jiazhu

AU - Yu, Bosco W. T.

AU - Pang, W. K.

PY - 2004/5

Y1 - 2004/5

N2 - We discuss the relationship between the marginal tail risk probability and the innovation’s tail risk probability for some stationary financial time series models. We first give the main results on the tail behavior of a class of infinite weighted sums of random variables with heavy-tailed probabilities. And then, the main results are applied to three important types of time series models: infinite order moving averages, the simple bilinear time series and the solutions of stochastic difference equations. The explicit formulas are given to describe how the marginal tail probabilities come from the innovation’s tail probabilities for these time series. Our results can be applied to the tail estimation of time series and are useful for risk analysis in finance.

AB - We discuss the relationship between the marginal tail risk probability and the innovation’s tail risk probability for some stationary financial time series models. We first give the main results on the tail behavior of a class of infinite weighted sums of random variables with heavy-tailed probabilities. And then, the main results are applied to three important types of time series models: infinite order moving averages, the simple bilinear time series and the solutions of stochastic difference equations. The explicit formulas are given to describe how the marginal tail probabilities come from the innovation’s tail probabilities for these time series. Our results can be applied to the tail estimation of time series and are useful for risk analysis in finance.

KW - risk analysis

KW - infinite weighted sum

KW - moving average

KW - bilinear model

KW - stochastic difference equation

KW - tail probability

KW - vague convergence

U2 - 10.1360/02ys0317

DO - 10.1360/02ys0317

M3 - Article

VL - 47

SP - 321

EP - 338

JO - Science China Mathematics

T2 - Science China Mathematics

JF - Science China Mathematics

SN - 1674-7283

IS - 3

ER -