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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (3): 77-87.doi: 10.6040/j.issn.1671-9352.0.2023.439

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混合误差下一阶适度爆炸自回归模型最小二乘估计

段体城1,许成凯1,鲁紫婕1,贾沛焱2,谢素雅1,杨文志1*   

  1. 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
  • 发布日期:2025-03-10
  • 通讯作者: 杨文志(1982— ),男,副教授,博士,研究方向为概率论与数理统计. E-mail:wzyang@ahu.edu.cn
  • 作者简介:段体城(2000— ),男,硕士研究生,研究方向为概率论与数理统计. E-mail:duanticheng00@163.com*通信作者:杨文志(1982— ),男,副教授,博士,研究方向为概率论与数理统计. E-mail:wzyang@ahu.edu.cn
  • 基金资助:
    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)

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

DUAN Ticheng1, XU Chengkai1, LU Zijie1, JIA Peiyan2, XIE Suya1, YANG Wenzhi1*   

  1. 1. School of Big Data and Statistics, Anhui University, Hefei 230601, Anhui, China;
    2. Wendian College, Anhui University, Hefei 230601, Anhui, China
  • Published:2025-03-10

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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。

关键词: 适度爆炸自回归, 最小二乘估计, 柯西分布, 混合序列

Abstract: The least squares(LS)estimator is studied for the first-order and mildly explosive autoregression with φ-mixing errors. Under some weak conditions of E(u1)=0, E(|u1|4)<∞ and φ(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.

Key words: mildly explosive autoregression, least squares estimator, Cauchy distribution, mixing sequence

中图分类号: 

  • O212.1
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