  We develop a new class of dynamic multivariate Poisson count models that
allow for fast online updating and we refer to these models as multivariate
Poisson-scaled beta (MPSB). The MPSB model allows for serial dependence in the
counts as well as dependence across multiple series with a random common
environment. Other notable features include analytic forms for state
propagation and predictive likelihood densities. Sequential updating occurs
through the updating of the sufficient statistics for static model parameters,
leading to a fully adapted particle learning algorithm and a new class of
predictive likelihoods and marginal distributions which we refer to as the
(dynamic) multivariate confluent hyper-geometric negative binomial distribution
(MCHG-NB) and the the dynamic multivariate negative binomial (DMNB)
distribution. To illustrate our methodology, we use various simulation studies
and count data on weekly non-durable goods consumer demand.
