基于稳定分布的ARCH模型均值检验变点  

Tests for the mean change-point in ARCH models with stable distribution innovations

作　　者：金浩[1] 张思[1] 

机构地区：[1]西安科技大学理学院,陕西西安710054

出　　处：《宝鸡文理学院学报（自然科学版）》2017年第3期1-6,共6页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：国家自然科学基金(No.71473194;71273206);陕西省教育厅科研计划项目(No.16JK1500);陕西省科技厅项目:(No.2013KJXX-40);陕西省自然科学基金(No.2017JM1042)

摘　　要：目的讨论噪声项是稳定分布的ARCH模型的均值变点检验,其中特征指数κ∈(1,2)。方法引入残量平方累积和统计量,在原假设条件成立时,证明其极限分布是Levy过程的泛函。结果蒙特卡罗数值模拟结果表明:统计量的势函数值不仅对样本容量及特征指数敏感,也依赖于均值变点的跳跃幅度。结论残量累积和统计量能有效地检验基于稳定分布的ARCH模型均值变点。Purpose-To discuss that the noise item is the mean change-point in ARCH models of stable distribution whose characteristic exponent k is an element of （1, 2）. Method--The statistic of cumulative sum （CUSUM） test for square residuals, which is true under null hypothesis, is introduced to prove that its limit- ing distribution is the functional of Levy processes. Result-The results of Monte Carlo Digital Simulation in- dicate that the value of potential function for the statistics is not only sensitive to the stable index sample size and characteristic exponent but also dependent on the leap range of mean change-point. Conclusion The RCUSQ statistic can effectively constitute a tool for testing the mean change point of ARCH model with stable distribution.

关 键 词：残量平方累积和检验 稳定分布 均值变点 

分 类 号：O212.9[理学—概率论与数理统计]