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If a transiting exoplanet has a moon, that moon could be detected directly from the transit it produces itself, or indirectly via the transit timing variations it produces in its parent planet. There is a range of parameter space where the Kepler Space Telescope is sensitive to the TTVs exomoons might produce, though the moons themselves would be too small to detect photometrically via their own transits. The Earth's Moon, for example, produces TTVs of 2.6 minutes amplitude by causing our planet to move around their mutual centre of mass. This is more than Kepler's short-cadence interval of 1 minute and so nominally detectable (if transit timings can be measured with comparable accuracy), even though the Moon's transit signature is only 7% that of Earth's, well below Kepler's nominal photometric threshold. Here we examine several Kepler systems, exploring the hypothesis that an exomoon could be detected solely from the TTVs it induces on its host planet. We compare this with the alternate hypothesis that the TTVs are caused by an non-transiting planet in the system. We examine 13 Kepler systems and find 8 where both hypotheses explain the observed TTVs equally well. Though no definitive exomoon detection can be claimed on this basis, the observations are nevertheless completely consistent with a dynamically stable moon small enough to fall below Kepler's photometric threshold for transit detection, and these systems warrant further observation and analysis.