  The extremal index $\theta$, a number in the interval $[0,1]$, is known to be
a measure of primal importance for analyzing the extremes of a stationary time
series. New rank-based estimators for $\theta$ are proposed which rely on the
construction of approximate samples from the exponential distribution with
parameter $\theta$ that is then to be fitted via the method of moments. The new
estimators are analyzed both theoretically as well as empirically through a
large-scale simulation study. In specific scenarios, in particular for time
series models with $\theta \approx 1$, they are found to be superior to recent
competitors from the literature.
