Abstract In this paper, new models are studied by proposing the family of generalized power series distributions with inflated parameter (IGPSD) for the innovation process of the INAR(1) model. The main properties of the process were established, such as mean, variance, autocorrelation and transition probability. The methods of estimation by Yule–Walker and the conditional maximum likelihood were used to estimate the parameters of the models. Two particular cases of the INAR ( 1 ) $\left(1\right)$ model with IGPSD innovation were studied, named IPoINAR ( 1 ) $\left(1\right)$ and IGeoINAR ( 1 ) $\left(1\right)$ . Finally, in the real data example, a good performance of the proposed new models was observed.

中文翻译：

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具有膨胀参数的INAR（1）过程广义幂级数创新

摘要本文通过提出带有膨胀参数的广义幂级数分布（IGPSD）族来研究INAR（1）模型的创新过程，从而研究了新模型。建立了过程的主要属性，例如均值，方差，自相关和转移概率。Yule-Walker的估计方法和条件最大似然用于估计模型的参数。研究了具有IGPSD创新的INAR（1）$ \ left（1 \ right）$模型的两个特殊情况，分别称为IPoINAR（1）$ \ left（1 \ right）$和IGeoINAR（1）$ \ left（1 \）右）$。最后，在实际数据示例中，观察到了所提出的新模型的良好性能。