  Motivated by the recent proposal that one can obtain quasi-periodic
oscillations (QPOs) by photon echoes manifesting as non-trivial features in the
autocorrelation function (ACF), we study the ACFs of the light curves of three
accreting black hole candidates and a neutron star already known to exhibit
QPOs namely, GRS 1915+105, XTE J1550-564, XTE J1859+226 and Cygnus X-2. We
compute and focus on the form of the ACFs in search of systematics or specific
temporal properties at the time scales associated with the known QPO
frequencies in comparison with the corresponding PDS. Even within our small
object sample we find both similarities as well as significant and subtle
differences in the form of the ACFs both amongst black holes and between black
holes and neutron stars to warrant a closer look at the QPO phenomenon in the
time domain: The QPO features manifest as an oscillatory behavior of the ACF at
lags near zero; the oscillation damps exponentially on time scales equal to the
inverse QPO width to a level of a percent or so. In black holes this
oscillatory behavior is preserved and easily discerned at much longer lags
while this is not the case for the neutron star system Cyg X-2. The ACF of GRS
1915+105 provides an exception to this general behavior in that its decay is
linear in time indicating an undamped oscillation of coherent phase. We present
simple ad hoc models that reproduce these diverse time domain behaviors and we
speculate that their origin is the phase coherence of the underlying
oscillation. It appears plausible that time domain analyses, complementary to
the more common frequency domain ones, could impose tighter constraints and
provide clues for the driving mechanisms behind the QPO phenomenon.
