We investigate the global activity patterns predicted from a model active region heated by distributions of nanoflares that have a range of average frequencies. The activity patterns are manifested in time lag maps of narrow-band instrument channel pairs. We combine an extrapolated magnetic skeleton with hydrodynamic and forward modeling codes to create a model active region, and apply the time lag method to synthetic observations. Our aim is to recover some typical properties and patterns of activity observed in active regions. Our key findings are: 1. Cooling dominates the time lag signature and the time lags between the channel pairs are generally consistent with observed values. 2. Shorter coronal loops in the core cool more quickly than longer loops at the periphery. 3. All channel pairs show zero time lag when the line-of-sight passes through coronal loop foot-points. 4. There is strong evidence that plasma must be re-energized on a time scale comparable to the cooling timescale to reproduce the observed coronal activity, but it is likely that a relatively broad spectrum of heating frequencies operates across active regions. 5. Due to their highly dynamic nature, we find nanoflare trains produce zero time lags along entire flux tubes in our model active region that are seen between the same channel pairs in observed active regions.