  Supermassive black hole binaries (SMBHBs) should be common in galactic nuclei
as a result of frequent galaxy mergers. Recently, a large sample of sub-parsec
SMBHB candidates was identified as bright periodically variable quasars in
optical surveys. If the observed periodicity corresponds to the redshifted
binary orbital period, the inferred orbital velocities are relativistic
(v/c~0.1). The optical and UV luminosities are expected to arise from gas bound
to the individual BHs, and would be modulated by the relativistic Doppler
effect. The optical and UV light curves should vary in tandem with relative
amplitudes which depend on the respective spectral slopes. We constructed a
control sample of 42 quasars with aperiodic variability, to test whether this
Doppler colour signature can be distinguished from intrinsic chromatic
variability. We found that the Doppler signature can arise by chance in ~20%
(~37%) of quasars in the nUV (fUV) band. These probabilities reflect the
limited quality of the control sample and represent upper limits on how
frequently quasars mimic the Doppler brightness+colour variations. We performed
separate tests on the periodic quasar candidates, and found that for the
majority, the Doppler boost hypothesis requires an unusually steep UV spectrum
or an unexpectedly large BH mass and orbital velocity. We conclude that at most
~1/3rd of these periodic candidates can harbor Doppler-modulated SMBHBs.
