Weak Convergence of the Sequential Empirical Processes of Residuals in Nonstationary Autoregressive Models
Weak Convergence of the Sequential Empirical Processes of Residuals in Nonstationary Autoregressive Models
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DOI：
10.1214/aos/1028144857
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发表时间：
1998-04
影响因子：
4.5
通讯作者：
S. Ling
中科院分区：
文献类型：
--
作者：
S. Ling
本文证明了序列经验过程的弱收敛性。非平稳自回归模型中估计残差的n。在某些正则条件下，证明了？n弱收敛到一个基弗过程时，特征多项式不包括单位根1，否则？n弱收敛于一个基弗过程加一个随机积分泛函.后者不仅不同于Koul和Levental对爆炸AR（1）模型给出的结果，也不同于Bai对平稳阿尔马模型给出的结果。
This paper establishes the weak convergence of the sequential empirical process ? n of the estimated residuals in nonstationary autoregressive models. Under some regular conditions, it is shown that ? n converges weakly to a Kiefer process when the characteristic polynomial does not include the unit root 1; otherwise ? n converges weakly to a Kiefer process plus a functional of stochastic integrals in terms of the standard Brownian motion. The latter differs not only from that given by Koul and Levental for an explosive AR(1) model but also from that given by Bai for a stationary ARMA model.