  As the number of known exoplanets continues to grow, the question as to
whether such bodies harbour satellite systems has become one of increasing
interest. In this paper, we explore the transit timing effects that should be
detectable due to an exomoon and predict a new observable. We first consider
transit time variation (TTV), where we update the model to include the effects
of orbital eccentricity. We draw two key conclusions: 1) In order to maintain
Hill stability, the orbital frequency of the exomoon will always be higher than
the sampling frequency. Therefore, the period of the exomoon cannot be reliably
determined from TTV, only a set of harmonic frequencies. 2) The TTV amplitude
is proportional to M_S a_S where M_S is the exomoon mass and a_S is the
semi-major axis of the moon's orbit. Therefore, M_S and a_S cannot be
separately determined. We go on to predict a new observable due to exomoons -
transit duration variation (TDV). We derive the TDV amplitude and conclude that
its amplitude is not only detectable, but the TDV signal will provide two
robust advantages: 1) The TDV amplitude is proportional to M_S a_S^{-1/2} and
therefore the ratio of TTV and TDV allows for a separate determination of M_S
and a_S. 2) TDV has a 90 degrees phase difference to the TTV signal, making it
an excellent complementary technique.
