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December, 1994 Weak Convergence of the Sequential Empirical Processes of Residuals in ARMA Models
Jushan Bai
Ann. Statist. 22(4): 2051-2061 (December, 1994). DOI: 10.1214/aos/1176325771

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.

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Jushan Bai. "Weak Convergence of the Sequential Empirical Processes of Residuals in ARMA Models." Ann. Statist. 22 (4) 2051 - 2061, December, 1994. https://doi.org/10.1214/aos/1176325771

Information

Published: December, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0826.60016
MathSciNet: MR1329182
Digital Object Identifier: 10.1214/aos/1176325771

Subjects:
Primary: 62G30
Secondary: 60F17 , 62F05 , 62M10

Keywords: Change-point problem , Kiefer process , residual analysis , sequential empirical process , time series models , weak convergence

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.22 • No. 4 • December, 1994
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