JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (7): 106-114.doi: 10.6040/j.issn.1671-9352.0.2022.198

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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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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

CLC Number: 

  • O213.1

Fig.1

Chart of the autocorrelation coefficient of AMD stock returns"

Fig.2

Line chart of AMD stock returns"

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