  The transient black hole binary XTE J1118+480 exhibited dramatic rapid
variability at all wavelengths which were suitably observed during its 2000
April-July outburst. We examine time-resolved X-ray, ultraviolet, optical, and
infrared data spanning the plateau phase of the outburst. We find that both
X-ray and infrared bands show large amplitude variability. The ultraviolet and
optical variability is more subdued, but clearly correlated with that seen in
the X-rays. The ultraviolet, at least, appears to be dominated by the
continuum, although the lines are also variable. Using the X-ray variations as
a reference point, we find that the UV variability at long wavelengths occurs
later than that at short wavelengths. Uncertainty in HST timing prohibits a
determination of the absolute lag with respect to the X-rays, however. The
transfer function is clearly not a delta-function, exhibiting significant
repeatable structure. For the main signal we can rule out an origin in
reprocessing on the companion star - the lack of variation in the lags is not
consistent with this given a relatively high orbital inclination. Weak
reprocessing from the disc and/or companion star may be present, but is not
required, and another component must dominate the variability. This could be
variable synchrotron emission correlated with X-ray variability, consistent
with our earlier interpretation of the IR flux as due to synchrotron emission
rather than thermal disc emission. In fact the broad-band energy distribution
of the variability from IR to X-rays is consistent with expectations of
optically thin synchrotron emission. We also follow the evolution of the
low-frequency quasi-periodic oscillation in X-rays, UV, and optical. Its
properties at all wavelengths are similar indicating a common origin.
