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The extremes of a stationary time series typically occur in clusters. Aprimary measure for this phenomenon is the extremal index, representing thereciprocal of the expected cluster size. Both a disjoint and a sliding blocksestimator for the extremal index are analyzed in detail. In contrast to manycompetitors, the estimators only depend on the choice of one parametersequence. We derive an asymptotic expansion, prove asymptotic normality andshow consistency of an estimator for the asymptotic variance. Explicitcalculations in certain models and a finite-sample Monte Carlo simulation studyreveal that the sliding blocks estimator outperforms other blocks estimators,and that it is competitive to runs- and inter-exceedance estimators in variousmodels. The methods are applied to a variety of financial time series.

Weak convergence of a pseudo maximum likelihood estimator for the extremal index