In this work we investigate the global activity patterns predicted from a model active region heated by distributions of nanoflares that have a range of frequencies. What differs is the average frequency of the distributions. The activity patterns are manifested in time lag maps of narrow-band instrument channel pairs. We combine hydrodynamic and forward modeling codes with a magnetic field extrapolation to create a model active region and apply the time lag method to synthetic observations. Our aim is not to reproduce a particular set of observations in detail, but to recover some typical properties and patterns observed in active regions. Our key findings are the following. (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 footpoints. (4) There is strong evidence that plasma must be re-energized on a timescale comparable to the cooling timescale to reproduce the observed coronal activity, but it is likely that a relatively broad spectrum of heating frequencies are operating 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.