Statistical inference for heavy tailed series with extremal independence

Abstract

We consider stationary time series $\{X_j,j\in Z\}whosefinitedimensionaldistributionsareregularlyvaryingwithextremalindependence.Weassumethatforeach$h \geq 1$,conditionallyon$X_0$toexceedathresholdtendingtoinfinity,theconditionaldistributionof$X_h$ suitably normalized converges weakly to a non degenerate distribution. We consider in this paper the estimation of the normalization and of the limiting distribution.

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• Stochastic volatility models with possible extremal clustering
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• Bootstrapping Empirical Processes of Cluster Functionals with Application to Extremograms