一类相依随机系数整数值二项自回归模型  

A Class of Integer-Valued Binomial Autoregressive Model with Dependent Random Coefficients

作　　者：于光 崔帅[2] 王德辉 YU Guang;CUI Shuai;Wang De-hui(College of Economics,Changchun University of Finance and Economics,Changchun 130012,China;School of Mathematics,Jilin University,Changchun 130012,China;School of Economics,Liaoning University,Shenyang 110036,China)

机构地区：[1]长春财经学院经济学院,吉林长春130012 [2]吉林大学数学学院,吉林长春130012 [3]辽宁大学经济学院,辽宁沈阳110036

出　　处：《数理统计与管理》2025年第2期266-276,共11页Journal of Applied Statistics and Management

基　　金：国家自然科学基金项目(12271231,12471249)。

摘　　要：为了精细刻画具有上限的整数值时间序列数据,本文提出了一类相依随机系数整数值二项自回归模型,证明了模型的严平稳遍历性,讨论了模型的转移概率、期望、方差等概率统计性质,基于条件最大似然法和条件最小二乘法研究了模型参数的估计问题,给出了相应的数值算法,并得到了估计量的渐近性质。通过数值模拟验证了估计的效果,并基于所提出的模型拟合了我国上海是和德国汉堡市的降雨量数据。实证研究结果表明,我们所提出的模型具有一定的竞争力。To accurately characterize the integer-valued time series data with a finite range,this paper proposes a class of integer-valued binomial autoregressive models with dependent random coefficients.The strict stationary and ergodicity properties of the model are proved.The probabilistic and statistics properties such as transition probability,expectation,and variance of the model are discussed.Based on the conditional maximum likelihood method and conditional least square method,the parameter estimation problems of model parameters are studied,the corresponding numerical algorithms are given,and the asymptotic properties of the estimators are obtained.The effect of the estimate is verified via numerical simulations.The rainfall data in Shanghai and Hamburg,Germany was fitted based on the proposed model.The results of empirical research show that the proposed model is competitive.

关 键 词：整数值时间序列 二项自回归模型 相依系数 随机系数 参数估计 

分 类 号：O212[理学—概率论与数理统计] O212.8[理学—数学]