In recent years, modelling count data has become one of the most important and popular topics in time‐series analysis. At the same time, variable selection methods have become widely used in many fields as an effective statistical modelling tool. In this paper, we consider using a variable selection method to solve a modelling problem regarding the first‐order Poisson integer‐valued autoregressive (PINAR(1)) model with covariables. The PINAR(1) model with covariables is widely used in many areas because of its practicality. When using this model to deal with practical problems, multiple covariables are added to the model because it is impossible to know in advance which covariables will affect the results. But the inclusion of some insignificant covariables is almost impossible to avoid. Unfortunately, the usual estimation method is not adequate for the task of deleting the insignificant covariables that cause statistical inferences to become biased. To overcome this defect, we propose a penalised conditional least squares (PCLS) method, which can consistently select the true model. The PCLS estimator is also provided and its asymptotic properties are established. Simulation studies demonstrate that the PCLS method is effective for estimation and variable selection. One practical example is also presented to illustrate the practicability of the PCLS method.

中文翻译：

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具有协变量的一阶Poisson整数值自回归模型的变量选择

近年来，建模计数数据已成为时间序列分析中最重要和最受欢迎的主题之一。同时，变量选择方法作为一种有效的统计建模工具已在许多领域广泛使用。在本文中，我们考虑使用变量选择方法来解决带有协变量的一阶Poisson整数值自回归（PINAR（1））模型的建模问题。具有协变量的PINAR（1）模型因其实用性而在许多领域得到了广泛使用。当使用此模型来处理实际问题时，会将多个协变量添加到模型中，因为无法提前知道哪些协变量会影响结果。但是，几乎不可能避免包含一些无关紧要的协变量。不幸，通常的估算方法不足以删除导致统计推断有偏见的无关紧要的变量。为了克服此缺陷，我们提出了一种惩罚条件最小二乘（PCLS）方法，该方法可以一致地选择真实模型。还提供了PCLS估计器，并建立了其渐近性质。仿真研究表明，PCLS方法对于估计和变量选择有效。还给出了一个实际的例子来说明PCLS方法的实用性。还提供了PCLS估计器，并建立了其渐近性质。仿真研究表明，PCLS方法对于估计和变量选择有效。还给出了一个实际的例子来说明PCLS方法的实用性。还提供了PCLS估计器，并建立了其渐近性质。仿真研究表明，PCLS方法对于估计和变量选择有效。还给出了一个实际的例子来说明PCLS方法的实用性。