We introduce a simple criterion for studying stationarity and moments properties of some multivariate Markovian autoregressive processes, under a contracting mapping assumption. We apply our results to the Poisson INGARCH model and to one of its multivariate extension recently introduced in the literature. In particular, we obtain optimal stationarity conditions and existence of some exponential moments.

中文翻译：

---

关于多变量非线性时间序列稳定性的注释以及计数时间序列的应用

我们引入了一个简单的标准，用于在收缩映射假设下研究一些多元马尔可夫自回归过程的平稳性和矩特性。我们将我们的结果应用于 Poisson INGARCH 模型及其最近在文献中引入的多元扩展之一。特别是，我们获得了最优平稳条件和一些指数矩的存在。