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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (7): 106-114.doi: 10.6040/j.issn.1671-9352.0.2022.198

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方差变点模型CUSUM型估计量的相合性

朱慧敏(),王梓楠,高敏,杨文志*()   

  1. 安徽大学数学科学学院, 安徽 合肥 230601
  • 收稿日期:2022-04-01 出版日期:2023-07-20 发布日期:2023-07-05
  • 通讯作者: 杨文志 E-mail:zhuimin1114@163.com;wzyang@ahu.edu.cn
  • 作者简介:朱慧敏(1995—)，女，硕士研究生，研究方向概率论与数理统计. E-mail: zhuimin1114@163.com
  • 基金资助:
    安徽省自然科学基金面上基金资助项目(2008085MA14);安徽大学大学生创新创业训练项目(202010357001);安徽省省级“双基”示范项目概率论(Y010512024/032)

The consistency of CUSUM-type estimator in variance change-point model

Huimin ZHU(),Zinan WANG,Min GAO,Wenzhi YANG*()   

  1. School of Mathematical Sciences, Anhui University, Hefei 230601, Anhui, China
  • Received:2022-04-01 Online:2023-07-20 Published:2023-07-05
  • Contact: Wenzhi YANG E-mail:zhuimin1114@163.com;wzyang@ahu.edu.cn

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摘要：

基于混合误差序列, 研究方差变点模型CUSUM型估计量的相合性问题。分别在高阶矩条件和低阶矩条件下, 获得CUSUM型估计量的强收敛速度和弱收敛速度, 推广了已有方差变点模型在误差满足独立同分布条件下获得的一些理论成果。作为应用, 利用方差变点方法对美国超威半导体公司股票收益率的波动率是否发生变化开展分析工作, 最终准确找到波动率发生变化的位置。

关键词: 方差变点模型, 混合序列, CUSUM型估计量, 收敛速度

Abstract:

The consistency problem of CUSUM-type estimator is investigated in the variance change-point model based on the mixing error sequences. The strong convergence rate and weak convergence rate for the CUSUM-type estimator are obtained by the high moment condition and low moment condition, respectively. It extends some theoretical results of the variance change-point model based on the independent and identically distributed errors. As an application, the variance change-point method is used to analyze whether the volatility of US Advanced Micro Devices? stock returns has changed. Then, the position of the change in volatility is found accurately.

Key words: variance change-point, mixing sequence, CUSUM type estimator, convergence rate

中图分类号: 

  • O213.1

图1

AMD股票收益率自相关系数图"

图2

AMD股票收益率折线图"

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