  We perform numerical calculations of the expected transit timing variations
(TTVs) induced on a Hot-Jupiter by an Earth-mass perturber. Motivated by the
recent discoveries of retrograde transiting planets, we concentrate on an
investigation of the effect of varying relative planetary inclinations, up to
and including completely retrograde systems. We find that planets in low order
(E.g. 2:1) mean-motion resonances (MMRs) retain approximately constant TTV
amplitudes for $0<\,^{\circ}i<170\,^{\circ}$, only reducing in amplitude for $i
> 170\,^{\circ}$. Systems in higher order MMRs (E.g. 5:1) increase in TTV
amplitude as inclinations increase towards $45\,^{\circ}$, becoming
approximately constant for $45 < i < 135$, and then declining for $i >
135\,^{\circ}$. Planets away from resonance slowly decrease in TTV amplitude as
inclinations increase from 0 to 180, where-as planets adjacent to resonances
can exhibit a huge range of variability in TTV amplitude as a function of both
eccentricity and inclination. For highly retrograde systems ($135\,^{\circ} < i
\leq 180\,^{\circ}$), TTV signals will be undetectable across almost the
entirety of parameter space, with the exceptions occurring when the perturber
has high eccentricity or is very close to a MMR. This high inclination decrease
in TTV amplitude (on and away from resonance) is important for the analysis of
the known retrograde and multi-planet transiting systems, as inclination
effects need to be considered if TTVs are to be used to exclude the presence of
any putative planetary companions: absence of evidence is not evidence of
absence.
