混合误差下一阶适度爆炸自回归模型最小二乘估计  

Least squares estimator of the first-order and mildly explosive autoregression with mixing errors

作　　者：段体城 许成凯 鲁紫婕 贾沛焱 谢素雅 杨文志[1] DUAN Ticheng;XU Chengkai;LU Zijie;JIA Peiyan;XIE Suya;YANG Wenzhi(School of Big Data and Statistics,Anhui University,Hefei 230601,Anhui,China;Wendian College,Anhui University,Hefei 230601,Anhui,China)

机构地区：[1]安徽大学大数据与统计学院,安徽合肥230601 [2]安徽大学文典学院,安徽合肥230601

出　　处：《山东大学学报(理学版)》2025年第3期77-87,共11页Journal of Shandong University(Natural Science)

基　　金：安徽省自然科学基金资助项目(2008085MA14);安徽大学大学生创新创业训练项目(202310357126)。

摘　　要：基于误差是φ-混合序列,研究一阶适度爆炸自回归模型回归系数最小二乘(least squares,LS)估计问题。在误差满足弱条件E(u1)=0,E(|u1|4)<∞和φ(n)=O(n-8)时,获得回归系数最小二乘估计的极限分布——柯西分布。通过数据模拟得到的模拟结果与理论结果一致。作为应用,利用一阶适度爆炸模型和自回归系数区间估计,研究英伟达股票2013—2023年的股价增长过程。The least squares(LS)estimator is studied for the first-order and mildly explosive autoregression withφ-mixing errors.Under some weak conditions of E(u1)=0,E(|u1|4)<∞andφ(n)=O(n-8),the limit distribution of standard Cauchy distribution is obtained for the LS estimator.Some simulations are given,which agree with the theory results.As an application,the first-order mildly explosive model and autoregressive coefficient interval estimation are used to study the growth process of share price for the NVIDIA corporation common stock from 2013 to 2023.

关 键 词：适度爆炸自回归 最小二乘估计 柯西分布 混合序列 

分 类 号：O212.1[理学—概率论与数理统计]