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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2023, Vol. 40 ›› Issue (6): 909-928.doi: 10.3969/j.issn.1005-3085.2023.06.005

• • 上一篇    下一篇

带单个变点AR(1)模型的统计推断

杨  磊1,2,  杨兰军1,2,  吴刘仓1,2   

  1. 1. 昆明理工大学理学院，昆明  650500
    2. 昆明理工大学应用统计学研究中心，昆明 650500
  • 收稿日期:2021-09-27 接受日期:2022-08-01 出版日期:2023-12-15 发布日期:2024-02-15
  • 通讯作者: 杨兰军 E-mail: ylyl0514@126.com
  • 基金资助:
    国家自然科学基金 (11861041).

Statistical Inference for AR(1) Models with Single Change-point

YANG Lei1,2,  YANG Lanjun1,2,  WU Liucang1,2   

  1. 1. Faculty of Science, Kunming University of Science and Technology, Kunming 650500
    2. Center for Applied Statistics, Kunming University of Science and Technology, Kunming 650500
  • Received:2021-09-27 Accepted:2022-08-01 Online:2023-12-15 Published:2024-02-15
  • Contact: L. Yang. E-mail address: ylyl0514@126.com
  • Supported by:
    The National Natural Science Foundation of China (11861041).

摘要：

变点时间序列一直是计量经济学、工程学和统计学的一个重要研究课题，在金融、气象和工业等领域有着广泛的应用。研究了带单个变点一阶自回归(AR(1))模型的统计推断问题。基于极大似然(或拟似然)方法，针对带单个变点AR(1)模型给出了参数估计表达式及自相关系数估计的一致性条件，同时得到了该条件下自相关系数极大似然(或拟似然)估计的渐近分布，并依此讨论了模型是否存在变点的假设检验及自相关系数变化增量的假设检验问题。最后通过数值模拟和上证综合指数日交易量的实证分析说明了所提理论和方法的有效性。

关键词: AR(1)模型, 变点, 参数估计, 假设检验, 渐近分布

Abstract:

Time series with change-points always are important topics in economics, engineering and statistics, which have been widely applied in financial, meteorological, industrial and other fields. In this paper, we study the statistical inference of the AR(1) models with single change-point. For the AR(1) models with single change-point, we provide the estimators and the consistency condition of the autocorrelation coefficient estimators based on maximum likelihood (quasi-likelihood) methods. Under the provided sufficient conditions, we establish that the asymptotic distribution of the estimators, the hypothesis test on whether there is a change-point in the models and the increment of autoregressive coefficients are discussed. Finally, some simulation results and the analysis of the daily trading data of Shanghai Composite Index show the effectiveness of the proposed theories and methods.

Key words: AR(1) model, change-point, parameter estimation, hypothesis test, asymptotic distribution

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