Testing for equality of simultaneously estimated extremal indices

Ferro and Segers (2003) proposes a method to estimate the extremal index. In this paper, we propose a test for comparing the values of simultaneously estimated extremal indices for the left and right tails. We use a simulation studies to examine the performance of different estimators for the extremal index. We use a bootstrapping method for the interexceedance times of extreme values to construct confidence intervals of the estimators. For the new test, we use the 'Stationary Bootstrap' (Politis and Romano (1994)) to obtain the standard error of the estimated difference between the two extremal indices. We use the research on the extremal index in Chernick et al. (1991) with our own choice of process in a simulation studies to assess the power of the test. We apply the proposed methods to temperature data and stock returns.