  We present cross-correlation studies of gamma-ray (0.1-300 GeV), X-ray
(0.2-10 keV) and optical (R-band) variability of a sample of 26 blazars during
2008-2016. The light curves are from Fermi-LAT, Swift-XRT, and the Yale-SMARTS
blazar monitoring program. We stack the discrete cross-correlation functions of
the blazars such that the features that are consistently present in a large
fraction of the sample become more prominent in the final result. We repeat the
same analysis for two subgroups, namely, low synchrotron peaked (LSP) and high
synchrotron peaked (HSP) blazars. We find that, on average, the variability at
multiple bands is correlated, with a time lag consistent with zero in both
subgroups. We describe this correlation with a leptonic model of non-thermal
emission from blazar jets. By comparing the model results with those from the
actual data we find that the inter-band cross-correlations are consistent with
an emission region of size nearly 0.1 pc within the broad line region for LSP
blazars. We rule out large changes of magnetic field (> 0.5 Gauss) across the
emission region or small values of magnetic field (e.g. 0.2 Gauss) for this
population. We also find that the observed variability of the HSP blazars can
be explained if the emission region is much larger than the distance to the
broad line region from the central black hole.
