As part of an effort to develop a systematic methodology for earthquake forecasting, we use a simple model of seismicity on the basis of 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 demonstrate the essential role played by the cascade of triggered seismicity in controlling the rate of aftershock decay as well as the overall level of seismicity in the presence of a constant external seismicity source. 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. Specifically, we find a prediction gain (defined as the ratio of the fraction of predicted events over the fraction of time in alarms) equal to 21 for a fraction of alarm of 1%, a target magnitude M ≥ 6, an update time of 0.5 days between two predictions, and for realistic parameters of the ETAS model. 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. Quantitatively, the fundamental limits of predictability found here are only lower bounds of the true values corresponding to the full information on the spatial location of earthquakes.