The extremal index (theta) is the key parameter for extending extreme value theory results from IID to stationary sequences. It determines the extent of clustering found in the largest observations of a stationary sequence {Xi}. This paper introduces an alternative interpretation of theta as a ratio of the limiting expected value of two random variables defined by extreme levels un, vn and a partition of the stationary sequence into blocks. These random variables consist on elements of the sequence of block maxima exceeding such levels. The estimator of theta derived from this interpretation is simple and follows a binomial distribution. This estimator is asymptotically unbiased in contrast to other estimators for theta (blocks method and runs method). Under certain conditions this methodology can be extended to moderately high levels u'n and v'n. The estimator obtained in this context is consistent. Furthermore, it has a binomial distribution that converges to a normal distribution with mean theta. This family of estimators outperform the rest of candidates commonly used to estimate theta. Some simulation experiments reinforce these findings. These experiments highlight the importance of block size selection and provide some guidance to proceed in practice with the estimation of the extremal index.
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