A New Family of Consistent and Asymptotically-Normal Estimators for the Extremal Index

The extremal index (θ) is the key parameter for extending extreme value theory results from i.i.d. to stationary sequences. One important property of this parameter is that its inverse determines the degree of clustering in the extremes. This article introduces a novel interpretation of the extremal index as a limiting probability characterized by two Poisson processes and a simple family of estimators derived from this new characterization. Unlike most estimators for θ in the literature, this estimator is consistent, asymptotically normal and very stable across partitions of the sample. Further, we show in an extensive simulation study that this estimator outperforms in finite samples the logs, blocks and runs estimation methods. Finally, we apply this new estimator to test for clustering of extremes in monthly time series of unemployment growth and inflation rates and conclude that runs of large unemployment rates are more prolonged than periods of high inflation.