AR(p)模型均值变点的CUSUM估计  

CUSUM Estimation of Mean Change Point in AR(p)Model

作　　者：许天明 魏岳嵩[1] 张婷婷 XU Tianming;WEI Yuesong;ZHANG Tingting(School of Mathematical Sciences,Huaibei Normal University,235000,Huaibei,Anhui,China)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《淮北师范大学学报（自然科学版）》2022年第4期1-5,共5页Journal of Huaibei Normal University：Natural Sciences

基　　金：安徽省高校自然科学基金项目(KJ2020A0024);安徽省高等学校省级质量工程项目(2020jxtd232,2020SJSFJXZZ353);淮北师范大学质量工程项目(2020xyylkc003,2020xylzy006);淮北师范大学研究生创新基金项目(cx2022036)。

摘　　要：由于AR(p)(自回归)模型在理论与实际中存在重要应用,故文章针对AR(p)(p阶自回归)模型中只存在一个均值变点的估计问题,利用CUSUM(累积和)法构建模型均值变点CUSUM估计量,并在一定假设条件下证明均值变点估计量的强相合性,并给出其强收敛速度.Due to AR(autoregressive)model has important applications in theory and pratice,CUSUM(cumula⁃tive sum)method is used to construct CUSUM estimator of model mean change point,aiming at the estima⁃tion problem that AR(p)(p-order autoregressive)model has only one mean change point.The properties of model mean change point estimator are obtained,which proves the strong consistency of change point estima⁃tor under certain assumptions and gives its strong convergence rate.

关 键 词：均值变点 累积和 强相合性 强收敛速度 

分 类 号：O212.1[理学—概率论与数理统计]