含均值变点时相依误差时间序列的Dickey-Fuller单位根统计量的极限分布  

Limit distribution of Dickey-Fuller unit root test statistics with dependent residuals and a mean shift

作　　者：杨晓蓉[1,2] 张立新[1] 

机构地区：[1]浙江大学数学系,浙江杭州310027 [2]浙江工商大学,统计与数学学院,浙江杭州310018

出　　处：《浙江大学学报（理学版）》2008年第6期614-617,共4页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(10471126;10671176)

摘　　要：均值带有变点的相依误差的自回归时间序列,在单位根假设条件下,自回归系数的正则化估计及其F统计量的极限分布可以表示成Wiener过程的泛函,其形式包含了变点前后的两个均值μ1和μ2.正则化估计的收敛速度在均值变点的影响下,达到Op(T-3/2)(其中T是样本容量).当μ1和μ2未知时,采用的最小二乘估计对这两个参数进行估计,其估计量μ1和μ2具有T～1/2相合性.The asymptotic behavior of autoregressive unit root test statistics with a mean shift is discussed. Under unit root hypothesis, the limiting distributions of the normalized estimator and the F-statistic can be expressed as functions of the Wiener process, which involves the pre-break mean μ1 , the post-break mean μ2 and the break fraction τ^＊. With a mean shift, the convergence rate of the normalized estimator could be much faster, up to Op （T^-3/2） （T is the sample size）. When μ1 and μ2 are unknown, the √T consistence of the proposed least squared estimators has been shown, which could be used to solve practical problems.

关 键 词：单位根 均值变点 Dickey Fuller检验统计量 F统计量 WIENER过程 

分 类 号：O211.4[理学—概率论与数理统计]