Abstract
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.
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