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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (3): 107-115.doi: 10.6040/j.issn.1671-9352.0.2023.541

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基于LSCUSUM方法的RCA(1)模型参数变点检验

侯成婷1,陈占寿1,2*   

  1. 1.青海师范大学数学与统计学院, 青海 西宁 810008;2.青海师范大学省部共建藏语智能信息处理及应用国家重点实验室, 青海 西宁 810008
  • 发布日期:2025-03-10
  • 通讯作者: 陈占寿(1982— ),男,教授,博士,研究方向为应用数理统计. E-mail:chenzhanshou@ 126.com
  • 作者简介:侯成婷(1999— ),女,硕士研究生,研究方向为应用数理统计. E-mail:980289934@qq.com*通信作者:陈占寿(1982— ),男,教授,博士,研究方向为应用数理统计. E-mail:chenzhanshou@ 126.com
  • 基金资助:
    国家自然科学基金资助项目(12161072);青海省自然科学基金资助项目(2024-ZJ-933)

Test of parameter change point in RCA(1)model based on LSCUSUM method

HOU Chengting1, CHEN Zhanshou1,2*   

  1. 1. School of Mathematics and Statistics, Qinghai Normal University, Xining 810008, Qinghai, China;
    2. The State Key Labora-tory of Tibetan Intelligent Information Processing and Application Jointly Built by Qinghai Normal University, Xining 810008, Qinghai, China
  • Published:2025-03-10

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摘要： 对一阶随机系数自回归模型(first-order random coefficient autoregressive model, RCA(1))的参数变点问题展开研究,提出了一种检验参数变点的基于位置和尺度的累积和(location and scale-based cumulative sum, LSCUSUM)检验统计量,在无变点原假设下推导出LSCUSUM统计量收敛于布朗桥的上界,并在备择假设下证明了该方法的一致性。数值模拟结果表明,LSCUSUM方法可以较好地控制经验水平,且相比RCA(1)模型参数变点的方法,经验势也有了一定程度的提高。最后通过所提方法分析了东晶电子股票的日收盘数据,检测出了该组数据中存在的变点。

关键词: 随机系数自回归模型, LSCUSUM统计量, 参数变点, 变点检验

Abstract: The parameter change point problem of the first-order random coefficient autoregressive(RCA(1))model is studied, and a location and scale based cumulative sum(LSCUSUM)test statistic is proposed to test the parameter change points. Under the null hypothesis of no change points, the convergence of the LSCUSUM statistic to the upper bound of the Brownian bridge is derived. Consistency of the method is established under the alternative hypothesis. Numerical simulation results demonstrate that the introduced LSCUSUM method effectively controls the empirical level. Furthermore, compared to existing methods for testing parameter change points in RCA(1)models, the proposed approach exhibits an enhanced empirical power. Finally, the method is applied to analyze daily closing data of Dongjing electronics stock, and detect the change points within the dataset.

Key words: random coefficient model, LSCUSUM test, parameter change point, change point test

中图分类号: 

  • O212.1
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