Most of the stationary first-order autoregressive integer-valued (INAR(1)) models were developed for a given thinning operator using either the forward approach or the backward approach. In the forward approach the marginal distribution of the time series is specified and an appropriate distribution for the innovation sequence is sought. Whereas in the backward setting, the roles are reversed. The common distribution of the innovation sequence is specified and the distributional properties of the marginal distribution of the time series are studied. In this article we focus on the backward approach in presence of the Binomial thinning operator. We establish a number of theoretical results which we proceed to use to develop stationary INAR(1) models with finite mean. We illustrate our results by presenting some new INAR(1) models that show underdispersion.

翻译：多数固定的一阶自动递减整值(INAR(1))模型是使用前方方法或后向方法为某个减瘦操作员开发的。在前方方法中,指定了时间序列的边际分布,并寻求对创新序列进行适当的分配。在后向环境中,作用被倒转。对创新序列的共同分布作了具体规定,并研究了时间序列边际分布的分布特性。在本条中,我们侧重于在Binomial瘦化操作员面前的后向方法。我们建立了一些理论结果,我们着手用这些结果来开发固定的 INAR(1) 模型,但有一定的平均值。我们通过展示一些显示细差的新的INAR(1)模型来说明我们的成果。