We propose a generalized mixture integer-valued generalized autoregressive conditional heteroscedastic model to provide a more flexible modeling framework. This model includes many mixture integer-valued models with different distributions already studied in the literature. The conditional and unconditional moments are discussed and the necessary and sufficient first- and second-order stationary conditions are derived. We also investigate the theoretical properties such as strict stationarity and ergodicity for the mixture process. The conditional maximum likelihood estimators via the EM algorithm are derived and the performances of the estimators are studied via simulation. The model can be selected in terms of both the number of mixture regimes and the number of orders in each regime by several different criteria. A real-life data example is also given to assess the performance of the model.

我们提出一种广义混合整数值广义自回归条件异方差模型，以提供更灵活的建模框架。该模型包括许多文献中已经研究过的具有不同分布的混合整数值模型。讨论了条件矩和无条件矩，并得出了必要的和足够的一阶和二阶平稳条件。我们还研究了混合过程的理论特性，例如严格的平稳性和遍历性。通过EM算法推导了条件最大似然估计量，并通过仿真研究了估计量的性能。可以根据混合方案的数量和每种方案中的订单数量，通过几种不同的标准来选择模型。