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Résumé 266 :

Extremal serial dependence of time series
Drees, Holger
University of Hamburg

The strength of the extremal dependence between consecutive observations in a time series can be described by the so-called coefficient of tail dependence $\eta$ introduced by Ledford and Tawn (1996). We analyze the asymptotic behavior of an estimator of $\eta$ in a nonparametric setting using empirical cluster processes that were introduced by Drees and Rootzén (2010). Moreover, the distribution of the estimation error is approximated using multiplier bootstrap techniques. In an application it is shown that a time series of financial returns exhibits weak extremal dependence that vanishes asymptotically, i.e.\ $\eta\in(1/2,1)$. These findings rule out both GARCH-type models (with $\eta=1$) and the usual stochastic volatility models ($\eta=1/2$), demonstrating that these standard models do not properly capture the extremal behavior of real financial time series.