Weak convergence of the sequential empirical processes of residuals in TAR models

详细信息    查看全文

• 作者：Dong Li (1)
  
• 关键词：Kiefer process ; sequential empirical process ; threshold autoregressive model ; weak convergence ; 62G30 ; 62G20
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2014
• 出版时间：January 2014
• 年：2014
• 卷：57
• 期：1
• 页码：173-180
• 全文大小：203 KB
• 作者单位：Dong Li (1)
  
  1. Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China
  
• ISSN：1869-1862

文摘

This paper studies the weak convergence of the sequential empirical process $\hat K_n$ of the residuals in the threshold autoregressive (TAR) model of order p. Under some mild conditions, it is shown that $\hat K_n$ converges weakly to a Kiefer process plus a random variable which converges to a multivariate normal. This differs from that given by Bai (1994) for a stationary autoregressive and moving average (ARMA) model.