Abstract
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.
Citation
Jushan Bai. "Weak Convergence of the Sequential Empirical Processes of Residuals in ARMA Models." Ann. Statist. 22 (4) 2051 - 2061, December, 1994. https://doi.org/10.1214/aos/1176325771
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