Abstract The efficient estimation problem of a semi-parametric periodic integer-valued autoregressive P I N A R p model of arbitrary order is considered. The unspecified distribution of the innovation process of this model is suposed to satisfy only some mild technical assumptions.We therefore provide efficient estimates for both parameters of the model, namely a periodic autoregressive parameters and a periodic probability law of the innovation non-negative integer values process which is seen as an infinite dimensional parameter. The performances of these efficient estimations are shown through an intensive simulation study and an application on real data set.

中文翻译：

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周期性 INARp 模型中的有效估计：非参数创新分布案例

摘要 研究了任意阶半参数周期整数值自回归PINAR p模型的有效估计问题。该模型的创新过程的未指定分布仅满足一些温和的技术假设。 因此，我们为模型的两个参数提供了有效的估计，即周期性自回归参数和创新非负整数值的周期性概率定律过程被视为无限维参数。通过深入的模拟研究和在真实数据集上的应用，展示了这些有效估计的性能。