  We develop a Bayesian hierarchical semiparametric model for phenomena related
to time series of counts. The main feature of the model is its capability to
learn a latent pattern of heterogeneity in the distribution of the process
innovation rates, which are softly clustered through time with the help of a
Dirichlet process placed at the top of the model hierarchy. The probabilistic
forecasting capabilities of the model are put to test in the analysis of crime
data in Pittsburgh, with favorable results.
