  This paper deals with the problem of model selection for a general class of
integer-valued time series.
  We propose a penalized criterion based on the Poisson quasi-likelihood of the
model.
  Under certain regularity conditions, the consistency of the procedure as well
as the consistency and the asymptotic normality of the Poisson quasi-likelihood
estimator of the selected model are established.
  Simulation experiments are conducted for some classical models such as
Poisson, binary INGARCH and negative binomial model with nonlinear dynamic.
Also, an application to a real dataset is provided.
