Comparing two block estimation procedures for the extremal index: An application

When extending the analysis of the limiting behaviour of the extreme values from independent and identically distributed sequences to stationary sequences a key parameter appears, the extremal index θ, whose accurate estimation is not easy and is not completely solved. Here we focus on the estimation of θ using blocks estimators, that can be constructed by using disjoint or sliding blocks. Both blocks construction require the choice of a threshold and a block length. The main objective of this work is to revisit another block estimation procedure that only depends on the block length, although some conditions on the underlying process need to be verified. An application will be presented for illustrating the proposed procedure.