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

• Bai, Jushan

## 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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File URL: http://mpra.ub.uni-muenchen.de/32915/1/MPRA_paper_32915.pdf
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## Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 32915.

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 Length: Date of creation: Aug 1991 Date of revision: 06 Jul 1993 Handle: RePEc:pra:mprapa:32915 Contact details of provider: Postal: Schackstr. 4, D-80539 Munich, GermanyPhone: +49-(0)89-2180-2219Fax: +49-(0)89-2180-3900Web page: http://mpra.ub.uni-muenchen.deMore information through EDIRC

## References

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1. J. Kreiss, 1991. "Estimation of the distribution function of noise in stationary processes," Metrika, Springer, vol. 38(1), pages 285-297, December.
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