  Bayesian computation for filtering and forecasting analysis is developed for
a broad class of dynamic models. The ability to scale-up such analyses in
non-Gaussian, nonlinear multivariate time series models is advanced through the
introduction of a novel copula construction in sequential filtering of coupled
sets of dynamic generalized linear models. The new copula approach is
integrated into recently introduced multiscale models in which univariate time
series are coupled via nonlinear forms involving dynamic latent factors
representing cross-series relationships. The resulting methodology offers
dramatic speed-up in online Bayesian computations for sequential filtering and
forecasting in this broad, flexible class of multivariate models. Two examples
in nonlinear models for very heterogeneous time series of non-negative counts
demonstrate massive computational efficiencies relative to existing
simulation-based methods, while defining similar filtering and forecasting
outcomes.
