  We compare the variability properties of very high energy gamma-ray emitting
BL Lac objects in the optical and radio bands. We use the variability
information to distinguish multiple emission components in the jet, to be used
as a guidance for spectral energy distribution modelling. Our sample includes
32 objects in the Northern sky that have data for at least 2 years in both
bands. We use optical R-band data from the Tuorla blazar monitoring program and
15 GHz radio data from the Owens Valley Radio Observatory blazer monitoring
program. We estimate the variability amplitudes using the intrinsic modulation
index, and study the time-domain connection by cross-correlating the optical
and radio light curves assuming power law power spectral density. Our sample
objects are in general more variable in the optical than radio. We find
correlated flares in about half of the objects, and correlated long-term trends
in more than 40% of the objects. In these objects we estimate that at least
10%-50% of the optical emission originates in the same emission region as the
radio, while the other half is due to faster variations not seen in the radio.
This implies that simple single-zone spectral energy distribution models are
not adequate for many of these objects.
