Checking the Dependency of E-coli Data with Extremal IndexUsing Block and Run Estimators

The extremal index characterizes the degree of local dependence in theextremes of a stationary time series. In this paper, we discuss an alternative interpre-tation of extremal index as a ratio of the limiting expected value of two random variabledefined by extreme levels and a partition of the stationary sequence into blocks. Weuse the run and the block definition for the cluster to analyse the clustering to find ex-tremal index. These experiments highlight the importance of block size selection. Thepractical implications are examined through the E-coli data from rivers in Selangor.