  BL Lacertae has been the target of several observing campaigns by the Whole
Earth Blazar Telescope (WEBT) collaboration and is one of the best studied
blazars at all accessible wavelengths. A recent analysis of the optical and
radio variability indicates that part of the radio variability is correlated
with the optical light curve. Here we present an analysis of a huge VLBI data
set including 108 images at 15, 22, and 43 GHz obtained between 1995 and 2004.
The aim of this study is to identify the different components contributing to
the single-dish radio light curves. We obtain separate radio light curves for
the VLBI core and jet and show that the radio spectral index of single-dish
observations can be used to trace the core variability. Cross-correlation of
the radio spectral index with the optical light curve indicates that the
optical variations lead the radio by about 100 days at 15 GHz. By fitting the
radio time lags vs. frequency, we find that the power law is steeper than
expected for a freely expanding conical jet in equipartition with energy
density decreasing as the square of the distance down the jet as in the
K\"onigl model. There is a section of the compact radio jet where the emission
is weak such that flares propagating down the jet are bright first in the core
region with a secondary increase in flux about 1.0 mas from the core. This
illustrates the importance of direct imaging to the interpretation of
multi-wavelength light curves that can be affected by several distinct
components at any given time. We discuss how the complex behaviour of the light
curves and correlations can be understood within the framework of a precessing
helical jet model.
