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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.

##### MSC:
 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)
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