  On the occasion of Laurens de Haan's 70th birthday, we discuss two aspects of
the statistical inference on the extreme value behavior of time series with a
particular emphasis on his important contributions. First, the performance of a
direct marginal tail analysis is compared with that of a model-based approach
using an analysis of residuals. Second, the importance of the extremal index as
a measure of the serial extremal dependence is discussed by the example of
solutions of a stochastic recurrence equation.
