Weak Convergence of the Sequential Empirical Processes of Residuals in ARMA Models

This paper studies the weak convergence of the sequential empirical process Kₙ of the estimated residuals in ARMA (p, q) models when the errors are independent and identically distributed. It is shown that, under some mild conditions, Kₙ converges weakly to a Kiefer process. The weak convergence is discussed for both finite and infinite variance time series models. An application to a change-point problem is considered.