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

Abstract

This paper studies the weak convergence of the sequential empirical process $\hat{K}_n$ 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, $\hat{K}_n$ 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.Time series models, residual analysis, sequential empirical process, weak convergence, Kiefer process, change-point problem