Abstract

This paper deals with the study of some probabilistic and statistical properties of some particular models of the class of Periodic Integer-Valued Autoregressive Moving Average, PINARMA(p, q), Models. For any considered particular model, the necessary and sufficient conditions for the periodically stationary in the first and second order, are established. The closed forms of the mean and the variance are obtained. The autocovariance structure is studied. The estimation of the parameters are obtained by the Yule-Walker (YW) method and the Conditional Least Squares (CLS) method. The performances of these estimators are assisted by a simulation illustration. Moreover, an application on real data set is provided.

摘要

本文涉及对周期性整数值自回归移动平均线PINARMA ( p , q ) 模型类的某些特定模型的一些概率和统计特性的研究。对于任何考虑的特定模型，建立一阶和二阶周期性平稳的充分必要条件。得到均值和方差的封闭形式。研究了自协方差结构。参数的估计是通过 Yule-Walker ( YW ) 方法和条件最小二乘法 ( CLS） 方法。这些估计器的性能由模拟插图辅助。此外，还提供了在真实数据集上的应用。