含有变点且序列方差不等下的2阶自回归模型研究  

Research on AR(2)Model with Change Point and Unequal Sequence Variances

作　　者：杨吉斌 张自武 黄达[2] YANG Jibin;ZHANG Ziwu;HUANG Da(Department of Mathematics and Data Science,Changji University,Changji 831100;Department of Mathematics and Physics,Xinjiang Institute of Engineering,Urumqi 830023)

机构地区：[1]昌吉学院数学与数据科学学院,新疆昌吉831100 [2]新疆工程学院数理学院,新疆乌鲁木齐830023

出　　处：《长江信息通信》2025年第2期57-60,共4页Changjiang Information & Communications

基　　金：自治区自然科学基金青年基金项目(NO.2019D01B10);自治区高校基本科研业务费项目(NO.XJEDU2022P116)。

摘　　要：本文研究了二阶自回归模型的序列变点的识别问题,且主要聚焦变点前后方差显著变化的复杂情形,提出了基于似然比检验的变点检测方法,通过比较分段模型与整体模型的似然函数值,实现变点位置的统计推断及参数估计。在模拟研究中,通过大量数据进行了验证,实验覆盖不同样本规模、变点位置及方差变化幅度,验证了方法的准确性与稳健性,同时结果表明,该方法能在复杂序列中精准定位变点并有效估计模型参数。另外敏感性分析揭示了变点位置估计精度与方差差异幅度相关,且随样本量增加显著提升。最后建议将变点检测纳入时间序列建模流程,以优化模型动态刻画能力与预测稳定性。本研究为经济、金融、气象等领域的时间序列分析提供了理论支撑与技术方案,对数据采集策略优化具有指导意义。This paper investigates the identification of sequence change points in second-order autoregressive models,primarily focusing on complex scenarios where significant variance changes occur before and after the change points.We propose a change point detection method based on likelihood ratio testing.By comparing the likelihood function values of the segmented model with those of the overall model,statistical inference of the change point location and parameter estimation can be achieved.In simulation studies,the method has been validated using a large amount of data,covering various sample sizes,change point locations,and amplitudes of variance variation.The accuracy and robustness of the method have been verified.The results also indicate that the method can accurately locate change points in complex sequences and effectively estimate model parameters.Additionally,sensitivity analysis reveals that the accuracy of change point location estimation is related to the magnitude of variance difference and significantly improves with increasing sample size.Finally,it is recommended to incorporate change point detection into the time series modeling process to optimize the model's dynamic characterization capability and prediction stability.This study provides theoretical support and technical solutions for time series analysis in fields such as economics,finance,and meteorology,and has guiding significance for optimizing data collection strategies.

关 键 词：二阶自回归模型 变点 参数估计 似然比检验 数据模拟 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]