We analyze the recently released CoGeNT data with a focus on their time-dependent properties. Using various statistical techniques, we confirm the presence of modulation in the data, and find a significant component at high (E_{ee} > 1.5$ keVee) energies. We find that standard elastic WIMPs in a Maxwellian halo do not provide a good description of the modulation. We consider the possibility of non-standard halos, using halo independent techniques, and find a good agreement with the DAMA modulation for Q_{Na} approx 0.3, but disfavoring interpretations with Q_{Na} = 0.5. The same techniques indicate that CDMS-Ge should see an O(1) modulation, and XENON100 should have seen 10-30 events (based upon the modulation in the 1.5-3.1 keVee range), unless L_{eff} is smaller than recent measurements. Models such as inelastic dark matter provide a good fit to the modulation, but not the spectrum. We note that tensions with XENON could be alleviated in such models if the peak is dominantly in April, when XENON data are not available due to noise.
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