  The tail index, indicating the degree of fatness of the tail distribution, is
an important component of extreme value theory since it dominates the
asymptotic distribution of extreme values such as the sample maximum. In this
paper, we consider the problem of testing for a change in the tail index of
time series data. As a test, we employ the cusum test and investigate its null
limiting distribution. Further, we derive the null limiting distribution of the
cusum test based on the residuals from autoregressive models. Simulation
results are provided for illustration.
