一阶广义零一堆积Poisson-Lindley整数值自回归模型的统计推断  

Statistical Inference for First-Order Generalized Zero-and-One Inflated Poisson-Lindley Integer-Valued Autoregressive Model

作　　者：张洁 杨志鹏 董小刚 ZHANG Jie;YANG Zhipeng;DONG Xiaogang(School of Mathematics and Statistics,Changchun University of Technology,Changchun 130012,China)

机构地区：[1]长春工业大学数学与统计学院,长春130012

出　　处：《吉林大学学报(理学版)》2025年第2期399-410,共12页Journal of Jilin University:Science Edition

基　　金：吉林省自然科学基金自由探索项目(批准号:YDZJ202301ZYTS384)。

摘　　要：针对过分散、零一堆积且个体之间具有相依结构的整数值时间序列数据的建模问题,提出一个具有零一堆积Poisson-Lindley新息的一阶广义整数值自回归模型.首先,给出模型的一些统计性质:期望、方差、自协方差和转移概率;其次,利用条件极大似然估计方法对模型的未知参数进行估计;最后,将该模型应用到一组实际数据中进行拟合,并用一些评估准则对模型进行验证.实例分析结果表明,该模型拟合效果较好.Aiming at the modeling problem of overdispersed,zero-and-one inflated integer-valued time series data with interdependent structures between individuals,we proposed a first-order generalized integer-valued autoregressive model with zero-and-one inflated Poisson-Lindley innovation.Firstly,we gave some statistical properties of the model,including expectation,variance,autocovariance,and transition probability.Secondly,the conditional maximum likelihood estimation method was used to estimate the unknown parameters of the model.Finally,the model was applied to a set of real data for fitting,and some evaluation criteria were used to verify the model.The case analysis results show that the model has a good fitting effect.

关 键 词：整数值时间序列 广义二项稀疏算子 零一堆积Poisson-Lindley 条件极大似然估计 

分 类 号：O212.1[理学—概率论与数理统计]