In practice it is important
to evaluate the impact of clusters of extreme observations caused by the dependence
in time series. The clusters contain consecutive exceedances of time series over
a threshold separated by return intervals with consecutive non-exceedances.
We derive asymptotically equal distributions of the number
of inter-arrival times between events of
interest arising both between two consecutive exceedances of a stationary process $\{R_n:n\ge 1\}$ and between two consecutive non-exceedances. It is found that the distributions are
geometric like
and corrupted by the extremal index. It is derived that the limit distribution tail of
the duration of clusters
that is
%are
defined as a sum
of the random number of the weakly dependent regularly varying inter-arrival times with tail index $0
