A common approach to analyze count time series is to fit models based on random sum operators. As an alternative, this paper introduces time series models based on a random multiplication operator, which is simply the multiplication of a variable operand by an integer-valued random coefficient, whose mean is the constant operand. Such operation is endowed into auto-regressive-like models with integer-valued random inputs, addressed as RMINAR. Two special variants are studied, namely the N0-valued random coefficient auto-regressive model and the N0-valued random coefficient multiplicative error model. Furthermore, Z-valued extensions are considered. The dynamic structure of the proposed models is studied in detail. In particular, their corresponding solutions are everywhere strictly stationary and ergodic, a fact that is not common neither in the literature on integer-valued time series models nor real-valued random coefficient auto-regressive models. Therefore, the parameters of the RMINAR model are estimated using a four-stage weighted least squares estimator, with consistency and asymptotic normality established everywhere in the parameter space. Finally, the new RMINAR models are illustrated with some simulated and empirical examples.

翻译：分析计数时间序列的常用方法是基于随机求和算子构建模型。作为替代方案，本文引入基于随机乘法算子的时间序列模型，该算子本质上是将变量操作数与整数值随机系数相乘（其均值为常数操作数）。该运算被嵌入具有整数值随机输入的自回归类模型中，称为RMINAR。研究探讨了两种特殊变体，即N0值随机系数自回归模型与N0值随机系数乘法误差模型，并进一步扩展到Z值情形。本文详细分析了所提模型的动态结构，特别指出其对应解在任意参数空间均满足严格平稳性与遍历性——这一特性在整数值时间序列模型文献或实值随机系数自回归模型中均不常见。因此，采用四阶段加权最小二乘估计器对RMINAR模型参数进行估计，并在整个参数空间上建立了估计量的一致性与渐近正态性。最后，通过模拟与实证案例验证了新型RMINAR模型的有效性。