  As part of an effort to develop a systematic methodology for earthquake
forecasting, we use a simple model of seismicity based on interacting events
which may trigger a cascade of earthquakes, known as the Epidemic-Type
Aftershock Sequence model (ETAS). The ETAS model is constructed on a bare
(unrenormalized) Omori law, the Gutenberg-Richter law and the idea that large
events trigger more numerous aftershocks. For simplicity, we do not use the
information on the spatial location of earthquakes and work only in the time
domain. We offer an analytical approach to account for the yet unobserved
triggered seismicity adapted to the problem of forecasting future seismic rates
at varying horizons from the present. Tests presented on synthetic catalogs
validate strongly the importance of taking into account all the cascades of
still unobserved triggered events in order to predict correctly the future
level of seismicity beyond a few minutes. We find a strong predictability if
one accepts to predict only a small fraction of the large-magnitude targets.
However, the probability gains degrade fast when one attempts to predict a
larger fraction of the targets. This is because a significant fraction of
events remain uncorrelated from past seismicity. This delineates the
fundamental limits underlying forecasting skills, stemming from an intrinsic
stochastic component in these interacting triggered seismicity models.
