  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 a disjoint and a 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.
