  The recurrence times between extreme events have been the central point of
statistical analyses in many different areas of science. Simultaneously, the
Poincar\'e recurrence time has been extensively used to characterize nonlinear
dynamical systems. We compare the main properties of these statistical methods
pointing out their consequences for the recurrence analysis performed in time
series. In particular, we analyze the dependence of the mean recurrence time
and of the recurrence time statistics on the probability density function, on
the interval whereto the recurrences are observed, and on the temporal
correlations of time series. In the case of long-term correlations, we verify
the validity of the stretched exponential distribution, which is uniquely
defined by the exponent $\gamma$, at the same time showing that it is
restricted to the class of linear long-term correlated processes. Simple
transformations are able to modify the correlations of time series leading to
stretched exponentials recurrence time statistics with different $\gamma$,
which shows a lack of invariance under the change of observables.
