Abstract

In this paper, we establish the consistency and the asymptotic normality of the Periodic Poisson (respectively the Periodic Geometric) Quasi Maximum Likelihood estimators, $(P-\mathcal{P}\mathit{QML})$ (respectively $(P-\mathcal{G}\mathit{QML})$, of a general class of periodic count time series models. In this class, the conditional mean is expressed as a parametric and measurable function, with periodic parameters, of the infinite past of the observed process. Applications for some particular periodic models of the class of Periodic Integer-Valued Autoregressive Moving Average, (PINARMA) models, are, under some regularity conditions, considered. The performances of these considered estimation methods are assisted by an intensive simulation study. Moreover, applications on two real datasets are provided.

摘要

在本文中，我们建立了周期性泊松（分别为周期性几何）准最大似然估计量的一致性和渐近正态性，$(磷-\mathcal{磷}\mathit{QML})$（分别$(磷-\mathcal{G}\mathit{QML})$，属于一般类的周期性计数时间序列模型。在这个类中，条件均值被表示为一个参数化和可测量的函数，具有周期性参数，是观察到的过程的无限过去。在某些规律性条件下，考虑了周期性整数值自回归移动平均线 ( PINARMA ) 模型类的某些特定周期性模型的应用。这些考虑过的估计方法的性能得到了深入的模拟研究的帮助。此外，还提供了在两个真实数据集上的应用。