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.

翻译：本文考虑使用多变点广义整数值自回归（MCP-GINAR）过程对一类非平稳计数时间序列进行建模的问题。应用最小描述长度原则（MDL）研究MCP-GINAR模型的统计推断，并分别在变点数量已知和未知的条件下建立了MDL模型选择过程的一致性结果。为寻找变点数量、变点位置、各段阶数及其参数的最优组合，本文采用带模拟退火的遗传算法求解这一困难优化问题。特别地，模拟退火过程弥补了传统遗传算法的早熟问题。仿真实验数值结果及三个真实数据分析实例表明，该过程具有优异的经验性能。