  We use time domain analysis techniques to investigate the rapid variability
of Cygnus X-1. We show that the cross-correlation functions between hard and
soft energy bands reach values very close to unity and peak at a lag of less
than 2 millisecond for energies separated by a factor of 10. This confirms that
the process that produces X-ray photons at different energies is extremely
coherent on short time scales and strongly constrains emission models proposed
to explain Fourier-frequency-dependent time lags. We present autocorrelation
functions at different energies, and note their widths decrease with increasing
energy. We show that the extended Compton corona model produces
auto-correlation functions whose widths increase with increasing energy, that
the model of cylindrical waves moving inward through a transition disk has too
large a peak lag in the cross-correlation function. Models of magnetic flaring
and of drifting blobs in a hot corona can qualitatively fit the observations.
