  Transit timing variations (TTVs) of exoplanets are normally interpreted as
the consequence of gravitational interaction with additional bodies in the
system. However, TTVs can also be caused by deformations of the system transits
by starspots, which might thus pose a serious complication in their
interpretation. We therefore simulate transit light curves deformed by
spot-crossing events for different properties of the stellar surface and the
planet, such as starspot position, limb darkening, planetary period, and impact
parameter. Mid-transit times determined from these simulations can be
significantly shifted with respect to the input values; these shifts cannot be
larger than ~1% of the transit duration and depend most strongly on the
longitudinal position of the spot during the transit and the transit duration.
Consequently, TTVs with amplitudes larger than the above limit are very
unlikely to be caused by starspots. We also investigate whether TTVs from
sequences of consecutive transits with spot-crossing anomalies can be
misinterpreted as the result of an additional body in the system. We use the
Generalized Lomb-Scargle periodogram to search for periods in TTVs and conclude
that low amplitude TTVs with statistically significant periods around active
stars are the most problematic cases. In those cases where the photometric
precision is high enough to inspect the transit shapes for deformations, it
should be possible to identify TTVs caused by starspots, however, especially
for cases with low transit signal to noise light curves (TSNR $\lesssim$ 15) it
becomes quite difficult to reliably decide whether these periods come from
starspots, physical companions in the system or if they are random noise
artifacts.
