  Many time series in natural and social sciences can be seen as resulting from
an interplay between exogenous influences and an endogenous organization. We
use a simple (ETAS) model of events occurring sequentially, in which future
events are influenced (partially triggered) by past events to ask the question
of how well can one disentangle the exogenous events from the endogenous ones.
We apply both model-dependant and model-independent stochastic declustering
methods to reconstruct the tree of ancestry and estimate key parameters. In
contrast with previously reported positive results, we have to conclude that
declustered catalogs are rather unreliable for the synthetic catalogs that we
have investigated, which contains of the order of thousands of events, typical
of realistic applications. The estimated rates of exogenous events suffer from
large errors. The key branching ratio $n$, quantifying the fraction of events
that have been triggered by previous events, is also badly estimated in general
from declustered catalogs. We find however that the errors tend to be smaller
and perhaps acceptable in some cases for small triggering efficiency and
branching ratios. The high level of randomness together with the very long
memory makes the stochastic reconstruction of trees of ancestry and the
estimation of the key parameters perhaps intrinsically unreliable for long
memory processes. For shorter memories (larger "bare" Omori exponent), the
results improve significantly.
