【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.更多还原

【Abstract】 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～1/2-consistence of the proposed least squared estimators has been shown, which could be used to solve practical problems.更多还原