  Blazars display strong variability on multiple timescales and in multiple
radiation bands. Their variability is often characterized by power spectral
densities (PSDs) and time lags plotted as functions of the Fourier frequency.
We develop a new theoretical model based on the analysis of the electron
transport (continuity) equation, carried out in the Fourier domain. The
continuity equation includes electron cooling and escape, and a derivation of
the emission properties includes light travel time effects associated with a
radiating blob in a relativistic jet. The model successfully reproduces the
general shapes of the observed PSDs and predicts specific PSD and time lag
behaviors associated with variability in the synchrotron, synchrotron
self-Compton (SSC), and external Compton (EC) emission components, from sub-mm
to gamma-rays. We discuss applications to BL Lacertae objects and to
flat-spectrum radio quasars (FSRQs), where there are hints that some of the
predicted features have already been observed. We also find that FSRQs should
have steeper PSD power-law indices than BL Lac objects at Fourier frequencies <
10^{-4} Hz, in qualitative agreement with previously reported observations by
the Fermi Large Area Telescope.
