期刊
ANNALS OF STATISTICS
卷 46, 期 5, 页码 2307-2335出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/17-AOS1621
关键词
Clusters of extremes; extremal index; stationary time series; mixing coefficients; block maxima
资金
- Collaborative Research Center Statistical modeling of nonlinear dynamic processes of the German Research Foundation (DFG) [SFB 823]
The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both disjoint and sliding blocks estimator for the extremal index are analyzed in detail. In contrast to many competitors, the estimators only depend on the choice of one parameter sequence. We derive an asymptotic expansion, prove asymptotic normality and show consistency of an estimator for the asymptotic variance. Explicit calculations in certain models and a finite-sample Monte Carlo simulation study reveal that the sliding blocks estimator outperforms other blocks estimators, and that it is competitive to runs- and inter-exceedance estimators in various models. The methods are applied to a variety of financial time series.
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