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

Abstract

The extremal index characterizes the degree of local dependence in the extremes of a stationary time series. In this paper, we discuss an alternative interpretation of extremal index as a ratio of the limiting expected value of two random variable defined by extreme levels and a partition of the stationary sequence into blocks. We use the run and the block definition for the cluster to analyse the clustering to find extremal index. These experiments highlight the importance of block size selection. The practical implications are examined through the E-coli data from rivers in Selangor. Keywords: Block and Run Estimators; Dependency; E-coli; Extremal Index 2010 Mathematics Subject Classification: 60G70; 62G32; 58E15