In recent years, there has been a considerable interest to study count time series with a dependence structure and appearance of excess of zeros values. Such series are commonly encountered in diverse disciplines, such as economics, financial research, environmental science, public health, among others. In this paper, we propose a stationary p-order integer-valued autoregressive process with zero-inflated Poisson innovations, called the ZINAR(p) times series model. We study some of its theoretical properties and develop a Markov chain Monte Carlo (MCMC) algorithm for inferring parameters from Bayesian perspectives. Finally, we demonstrate the utility of proposed ZINAR(p) model through simulated and real data examples.

中文翻译：

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具有零膨胀泊松创新的 p 阶整数值 AR 过程的贝叶斯分析

近年来，人们对研究具有相关结构和出现超过零值的计数时间序列产生了相当大的兴趣。此类系列在不同学科中很常见，例如经济学、金融研究、环境科学、公共卫生等。在本文中，我们提出了一种具有零膨胀泊松创新的平稳 p 阶整数值自回归过程，称为 ZINAR(p) 时间序列模型。我们研究了它的一些理论特性，并开发了一种马尔可夫链蒙特卡罗 (MCMC) 算法，用于从贝叶斯角度推断参数。最后，我们通过模拟和真实数据示例证明了所提出的 ZINAR(p) 模型的实用性。