zbMATH — the first resource for mathematics

Weak convergence of the sequential empirical processes of residuals in ARMA models. (English) Zbl 0826.60016
Summary: This paper studies the weak convergence of the sequential empirical process \(\widehat K_n\) of the estimated residuals in \(\text{ARMA} (p,q)\) 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.

60F05 Central limit and other weak theorems
62G30 Order statistics; empirical distribution functions
60F17 Functional limit theorems; invariance principles
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
Full Text: DOI