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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Li, D. Weak convergence of the sequential empirical processes of residuals in TAR models. Sci. China Math. 57, 173–180 (2014). https://doi.org/10.1007/s11425-013-4729-3
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DOI: https://doi.org/10.1007/s11425-013-4729-3