  Several authors have shown that precise measurements of transit time
variations of exoplanets can be sensitive to other planetary bodies, such as
exo-moons. In addition, the transit timing variations of the exoplanets closest
to their host stars can provide tests of tidal dissipation theory. These
studies, however, have not considered the effect of the host star. There is a
large body of observational evidence that eclipse times of binary stars can
vary dramatically due to variations in the quadrupole moment of the stars
driven by stellar activity. In this paper we investigate and estimate the
likely impact such variations have on the transit times of exoplanets. We find
in several cases that such variations should be detectable. In particular, the
estimated period changes for WASP-18b are of the same order as those expected
for tidal dissipation, even for relatively low values of the tidal dissipation
parameter. The transit time variations caused by the Applegate mechanism are
also of the correct magnitude and occur on timescales such that they may be
confused with variations caused by light-time travel effects due to the
presence of a Jupiter-like second planet. Finally, we suggest that transiting
exoplanet systems may provide a clean route (compared to binaries) to
constraining the type of dynamo operating in the host star.
