The extremal index \(\theta \in [0,1]\) characterizes the degree of local dependence in the
extremes of a stationary time series. The index of 1 means that exceedances occur singly in the
limit, while the index of value less than 1 implies that exceedances tend to occur in clusters.
The extremal index can be interpreted as:
the reciprocal of the limiting mean number of exceedances in blocks (i.e., cluster size) with
at least one exceedance; or
the limiting probability that an exceedance is followed by a run of observations below the
the times between exceedances over a high threshold.