  Stochastic variational inference algorithms are derived for fitting various
heteroskedastic time series models. We examine Gaussian, t, and skew-t response
GARCH models and fit these using Gaussian variational approximating densities.
We implement efficient stochastic gradient ascent procedures based on the use
of control variates or the reparameterization trick and demonstrate that the
proposed implementations provide a fast and accurate alternative to Markov
chain Monte Carlo sampling. Additionally, we present sequential updating
versions of our variational algorithms, which are suitable for efficient
portfolio construction and dynamic asset allocation.
