Bai, Jushan (1991): Weak convergence of the sequential empirical processes of residuals in ARMA models. Published in: Annals of Statistics , Vol. 22, (1994): pp. 20512061.

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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 changepoint problem is considered.
Item Type:  MPRA Paper 

Original Title:  Weak convergence of the sequential empirical processes of residuals in ARMA models 
Language:  English 
Keywords:  Time series models, residual analysis, sequential empirical process, weak convergence, Kiefer process, changepoint problem 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General C  Mathematical and Quantitative Methods > C2  Single Equation Models; Single Variables > C22  TimeSeries Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models 
Item ID:  32915 
Depositing User:  Jushan Bai 
Date Deposited:  20. Aug 2011 16:50 
Last Modified:  15. Feb 2013 06:50 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/32915 