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

Bai, Jushan (1991): Weak convergence of the sequential empirical processes of residuals in ARMA models. Published in: Annals of Statistics , Vol. 22, (1994): pp. 2051-2061.

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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.

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