  We study the out-of-equilibrium aging dynamics of the Random Energy Model
(REM) ruled by a single spin-flip Metropolis dynamics. We focus on the
dynamical evolution taking place on time-scales diverging with the system size.
Our aim is to show to what extent the activated dynamics displayed by the REM
can be described in terms of an effective trap model. We identify two time
regimes: the first one corresponds to the process of escaping from a basin in
the energy landscape and to the subsequent exploration of high energy
configurations, whereas the second one corresponds to the evolution from a deep
basin to the other. By combining numerical simulations with analytical
arguments we show why the trap model description does not hold in the former
but becomes exact in the second.
