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.
Publié le : 1994-12-14
Classification:
Time series models,
residual analysis,
sequential empirical process,
weak convergence,
Kiefer process,
change-point problem,
62G30,
60F17,
62M10,
62F05
@article{1176325771,
author = {Bai, Jushan},
title = {Weak Convergence of the Sequential Empirical Processes of Residuals in ARMA Models},
journal = {Ann. Statist.},
volume = {22},
number = {1},
year = {1994},
pages = { 2051-2061},
language = {en},
url = {http://dml.mathdoc.fr/item/1176325771}
}
Bai, Jushan. Weak Convergence of the Sequential Empirical Processes of Residuals in ARMA Models. Ann. Statist., Tome 22 (1994) no. 1, pp. 2051-2061. http://gdmltest.u-ga.fr/item/1176325771/