The extremogram and the cross-extremogram for a bivariate GARCH(1, 1) process

Muneya  Matsui; Thomas Valentin Mikosch

doi:10.1017/apr.2016.51

The extremogram and the cross-extremogram for a bivariate GARCH(1, 1) process

Muneya Matsui, Thomas Valentin Mikosch

Institut for Matematiske Fag

5 Citationer (Scopus)

Abstract

We derive asymptotic theory for the extremogram and cross-extremogram of a bivariate GARCH(1, 1) process. We show that the tails of the components of a bivariate GARCH(1, 1) process may exhibit power-law behavior but, depending on the choice of the parameters, the tail indices of the components may differ. We apply the theory to five-minute return data of stock prices and foreign-exchange rates. We judge the fit of a bivariate GARCH(1, 1) model by considering the sample extremogram and crossextremogram of the residuals. The results are in agreement with the independent and identically distributed hypothesis of the two-dimensional innovations sequence. The cross-extremograms at lag zero have a value significantly distinct from zero. This fact points at some strong extremal dependence of the components of the innovations.

Originalsprog	Engelsk
Tidsskrift	Advances in Applied Probability
Vol/bind	48
Udgave nummer	A
Sider (fra-til)	217 - 233
ISSN	0001-8678
DOI	https://doi.org/10.1017/apr.2016.51
Status	Udgivet - 2016

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10.1017/apr.2016.51

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/239B667EB358A735CC31BBBA8EAF7D56/S0001867816000513a.pdf/div-class-title-the-extremogram-and-the-cross-extremogram-for-a-bivariate-garch-1-1-process-div.pdf

Citationsformater

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AB - We derive asymptotic theory for the extremogram and cross-extremogram of a bivariate GARCH(1, 1) process. We show that the tails of the components of a bivariate GARCH(1, 1) process may exhibit power-law behavior but, depending on the choice of the parameters, the tail indices of the components may differ. We apply the theory to five-minute return data of stock prices and foreign-exchange rates. We judge the fit of a bivariate GARCH(1, 1) model by considering the sample extremogram and crossextremogram of the residuals. The results are in agreement with the independent and identically distributed hypothesis of the two-dimensional innovations sequence. The cross-extremograms at lag zero have a value significantly distinct from zero. This fact points at some strong extremal dependence of the components of the innovations.

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The extremogram and the cross-extremogram for a bivariate GARCH(1, 1) process

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