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

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 di...

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Bibliographic Details
Published inAdvances in applied probability Vol. 48; no. A; pp. 217 - 233
Main Authors Matsui, Muneya, Mikosch, Thomas
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.07.2016
Subjects
Autoregressive processes
Bivariate analysis
Hedging
Probability
Stochastic models
Volatility
60G10
bivariate GARCH(1,1)
Kesten's theorem
extremal dependence
Primary 60G70
Secondary 62M10
Regular variation
91B84
extremogram
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Summary: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 cross-extremogram 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.
ISSN:0001-8678
1475-6064
DOI:10.1017/apr.2016.51