We propose a goodness-of-fit test for a class of count time series models with covariates which includes the Poisson autoregressive model with covariates (PARX) as a special case. The test criteria are derived from a specific characterization for the conditional probability generating function and the test statistic is formulated as a $L_2$ weighting norm of the corresponding sample counterpart. The asymptotic properties of the proposed test statistic are provided under the null hypothesis as well as under specific alternatives. A bootstrap version of the test is explored in a Monte--Carlo study and illustrated on a real data set on road safety.

翻译：本文提出了一类含协变量的计数时间序列模型的拟合优度检验方法，该类模型以含协变量的泊松自回归模型（PARX）为特例。检验准则基于条件概率生成函数的特定刻画，检验统计量构造为相应样本对应的$L_2$加权范数。本文给出了在原假设及特定备择假设下所提检验统计量的渐近性质。通过蒙特卡洛研究探讨了该检验的Bootstrap版本，并将其应用于道路安全的真实数据集中进行验证。