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.
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