Li Cong, Zhang Haixiang, Wang Dehui
Center for Applied Statistical Research, School of Mathematics, Jilin University, Changchun, People's Republic of China.
Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, People's Republic of China.
J Appl Stat. 2021 Feb 15;49(7):1821-1847. doi: 10.1080/02664763.2021.1884206. eCollection 2022.
To analyse count time series data inflated at the + 1 values , we propose a new first-order integer-valued autoregressive process with -geometrically inflated Poisson innovations. Some statistical properties together with conditional maximum likelihood estimate are provided. For the purpose of statistical monitoring, we focus on the cumulative sum chart, exponentially weighted moving average chart and combined jumps chart towards the proposed process. Numerical simulations indicate that the conditional maximum likelihood estimator is unbiased. Moreover, the cumulative sum chart is the best choice to monitor our model in practice. Some applications about telephone complaints data are provided to illustrate the proposed methods.
为了分析在 +1 值处膨胀的计数时间序列数据，我们提出了一种新的一阶整数值自回归过程，其创新项为几何膨胀泊松分布。给出了一些统计性质以及条件最大似然估计。出于统计监测的目的，我们针对所提出的过程重点研究累积和控制图、指数加权移动平均控制图和组合跳跃控制图。数值模拟表明条件最大似然估计量是无偏的。此外，累积和控制图在实际中是监测我们模型的最佳选择。提供了一些关于电话投诉数据的应用来阐述所提出的方法。
