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

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.