  This article considers the problem of modeling a class of nonstationary count
time series using multiple change-points generalized integer-valued
autoregressive (MCP-GINAR) processes. The minimum description length principle
(MDL) is applied to study the statistical inference for the MCP-GINAR model,
and the consistency results of the MDL model selection procedure are
established respectively under the condition of known and unknown number of
change-points. To find the ``best" combination of the number of change-points,
the locations of change-points, the order of each segment and its parameters, a
genetic algorithm with simulated annealing is implemented to solve this
difficult optimization problem. In particular, the simulated annealing process
makes up for the precocious problem of the traditional genetic algorithm.
Numerical results from simulation experiments and three examples of real data
analyses show that the procedure has excellent empirical properties.
