基于Bootstrap抽样的厚尾自回归过程结构变点检测  

Structural change-point detection for heavy-tailed autoregressive process based on Bootstrap sampling

作　　者：张思[1] 金浩[1] 杨云锋[1] ZHANG Si;JIN Hao;YANG Yunfeng(School of Science,Xi'an University of Science and Technology,Xi'an 710054,Shaanxi,China)

机构地区：[1]西安科技大学理学院,西安710054

出　　处：《华中师范大学学报（自然科学版）》2023年第4期483-493,共11页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(71473194);陕西省科技厅自然科学基金项目(2020JM513).

摘　　要：该文考虑了具有稳定分布的p阶自回归过程均值变点检验问题.通过构造修正的比值型检验统计量,利用广义的中心极限定理,证明统计量在原假设下的渐近分布是列维过程的泛函,并得到了其在备择假设下的一致性.针对渐近分布依赖未知参数的情况,采用Bootstrap抽样逼近渐近分布以得到更精确的临界值.数值仿真结果表明,基于Bootstrap抽样的Ratio检验不仅很好地控制了经验水平,经验势也达到令人满意的效果.此外,当突变位置位于样本后半段时,经验势有较大幅度提高.最后,通过一组美国铝业收盘价数据进一步验证本文所提的变点检验方法的有效性和可行性.In this paper,the problem of the mean change point test of the p-order autoregressive process with stable distribution is considered.By constructing the modified ratio test statistic and using the generalized central limit theorem,it is proved that the asymptotic distribution of the statistic under the null hypothesis is a functional of Lévy distribution,and its consistency under the alternative hypothesis is obtained.For the case that the asymptotic distribution depends on unknown parameters,the Bootstrap sampling is used to approximate the asymptotic distribution to obtain more accurate critical values.The numerical simulation results show that the ratio test based on Bootstrap sampling not only controls the empirical sizes well,but also the empirical powers achieves satisfactory results.In addition,when the mutation position is located in the second half of the sample,the empirical powers is greatly improved.Finally,a set of Alcoa s closing prices further verifies the validity and feasibility of the change point test method proposed in this paper.

关 键 词：厚尾序列 均值变点 比值型检验 BOOTSTRAP 

分 类 号：O212[理学—概率论与数理统计]