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In extreme value statistics for stationary sequences, blocks estimators areusually constructed by using disjoint blocks because exceedances over highthresholds of different blocks can be assumed asymptotically independent. Inthis paper we focus on the estimation of the extremal index which measures thedegree of clustering of extremes. We consider disjoint and sliding blocksestimators and compare their asymptotic properties. In particular we show thatthe sliding blocks estimator is more efficient than the disjoint version andhas a smaller asymptotic bias. Moreover we propose a method to reduce its biaswhen considering sufficiently large block sizes.

A Sliding Blocks Estimator for the Extremal Index