  This paper develops forecasting methodology and application of new classes of
dynamic models for time series of non-negative counts. Novel univariate models
synthesise dynamic generalized linear models for binary and conditionally
Poisson time series, with dynamic random effects for over-dispersion. These
models allow use of dynamic covariates in both binary and non-zero count
components. Sequential Bayesian analysis allows fast, parallel analysis of sets
of decoupled time series. New multivariate models then enable information
sharing in contexts when data at a more highly aggregated level provide more
incisive inferences on shared patterns such as trends and seasonality. A novel
multi-scale approach-- one new example of the concept of decouple/recouple in
time series-- enables information sharing across series. This incorporates
cross-series linkages while insulating parallel estimation of univariate
models, hence enables scalability in the number of series. The major motivating
context is supermarket sales forecasting. Detailed examples drawn from a case
study in multi-step forecasting of sales of a number of related items showcase
forecasting of multiple series, with discussion of forecast accuracy metrics
and broader questions of probabilistic forecast accuracy assessment.
