周期随机系数自回归模型的统计推断  

Statistical Inference of Periodic Random Coefficient Autoregressive Model

作　　者：赵志文[1] 徐圣楠 Zhao Zhiwen;Xu Shengnan(School of Mathematics,Jilin Normal University,Siping Jilin 136000,China)

机构地区：[1]吉林师范大学数学学院,吉林四平136000

出　　处：《统计与决策》2022年第4期50-54,共5页Statistics & Decision

基　　金：国家自然科学基金资助项目(11571138);吉林省自然科学基金资助项目(20210101151JC)。

摘　　要：文章研究了一阶周期随机系数自回归模型的性质和参数估计问题。首先讨论了该模型均值函数、方差函数以及协方差函数的周期平稳性。其次讨论了当误差服从正态分布时模型参数的估计问题,给出了模型参数的矩估计和最小二乘估计,并通过随机模拟对这两种估计方法进行比较。最后将上述方法用于实际数据的建模拟合分析。结果表明所提出方法具有较小的误差。This paper studies the properties and parameter estimation of first-order periodic random coefficient autoregressive model. Firstly, the periodic stationarity of mean function, variance function and covariance function is discussed. Secondly,the parameter estimation of the model is discussed when the errors follow normal distribution;the moment estimation and least square estimation of parameters of the model are given, and the two estimation methods are compared by random simulation. Finally, the above methods are applied to the construction and simulation analysis of real data. The results show that the error of the proposed method is small.

关 键 词：周期随机系数自回归模型 周期平稳性 矩估计 最小二乘法 

分 类 号：O212.1[理学—概率论与数理统计]