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

The Annals of Statistics · 1994 · Volume 22 · Issue 4

Abstract

This paper studies the weak convergence of the sequential empirical process $\widehat{K}_n$ 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, $\widehat{K}_n$ 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.

Keywords

60F17; 62F05; 62G30; 62M10; Change-point problem; Kiefer process; residual analysis; sequential empirical process; time series models; weak convergence;

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