This paper proposes a penalized maximum quasi-likelihood (PMQL) estimation that can solve the problem of order selection and parameter estimation regarding the pth-order integer-valued time series models. The PMQL estimation can effectively delete the insignificant orders in model. By contrast, the significant orders can be retained and their corresponding parameters are estimated, simultaneously. Moreover, the PMQL estimation possesses certain robustness hence its order shrinkage effectiveness is superior to the traditional penalized estimation method even if the data is contaminated. The theoretical properties of the PMQL estimator, including the consistency and oracle properties, are also investigated. Numerical simulation results show that our method is effective in a variety of situations. The Westgren’s data set is also analyzed to illustrate the practicability of the PMQL method.

中文翻译：

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整数值时间序列模型订单收缩和通过惩罚拟似然方法选择

本文提出了一种惩罚最大拟似然（PMQL）估计，它可以解决关于 p 阶整数值时间序列模型的顺序选择和参数估计问题。PMQL 估计可以有效地删除模型中不重要的阶数。相比之下，可以保留重要订单并同时估计其相应的参数。此外，PMQL估计具有一定的鲁棒性，因此即使数据受到污染，其订单收缩效果也优于传统的惩罚估计方法。还研究了 PMQL 估计器的理论特性，包括一致性和预言机特性。数值模拟结果表明，我们的方法在多种情况下都是有效的。