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

Research output: Contribution to journalArticle

3 Citations (Scopus)

### 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.
Original language English 749-760 12 Science China Mathematics 45 6 https://doi.org/10.1360/02ys9082 Published - Jun 2002

### Fingerprint

Tail Dependence
Bilinear Model
Random variable
First-order
Stationary Time Series
Nonlinear Time Series
Conditional probability
Finance
Explicit Formula
Tail
Dependent
Model
Class
Tail dependence
Random variables
Innovation
Meaning

### Keywords

• ARCH
• bilinear model
• dependence
• tail probability

### Cite this

@article{da4a9554da7d4ecbb9099b00b20273bf,
title = "Tail dependence of random variables from ARCH and heavy-tailed Bilinear models",
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.",
keywords = "ARCH , bilinear model, dependence , tail probability",
author = "Jiazhu Pan",
year = "2002",
month = "6",
doi = "10.1360/02ys9082",
language = "English",
volume = "45",
pages = "749--760",
journal = "Science China Mathematics",
issn = "1674-7283",
number = "6",

}

In: Science China Mathematics, Vol. 45, No. 6, 06.2002, p. 749-760.

Research output: Contribution to journalArticle

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

JF - Science China Mathematics

SN - 1674-7283

IS - 6

ER -