In this paper we introduce a new integer valued autoregressive model of order one. The specificity of this model is based on its non-linear structure. The autoregressive component is defined through the binomial thinning operator. Also, an additional process is introduced into the autoregressive component. This random process controls how the previous value influences the next value of the observed series. For such a model, the main properties are derived and the unknown parameters of the model are estimated using the conditional maximum likelihood method. The practical aspect of the model is discussed on real data sets.

中文翻译：

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非线性随机环境INAR（1）模型

在本文中，我们介绍了一种新的一阶整数值自回归模型。该模型的特异性基于其非线性结构。自回归分量是通过二项式稀疏运算符定义的。另外，将附加过程引入自回归组件。此随机过程控制前一个值如何影响观察到的序列的下一个值。对于这样的模型，使用条件最大似然方法导出主要属性，并估计模型的未知参数。在实际数据集上讨论了模型的实际方面。