# Weak convergence of the sequential empirical processes of residuals in ARMA models

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Abstract

This paper studies the weak convergence of the sequential empirical process $\hat{K} n$ of the estimated residuals inARMAp,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 change-point 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, change-point problem-

Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: GeneralC - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes-

Autor: Bai, Jushan

Fuente: https://mpra.ub.uni-muenchen.de/32915/