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

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  • Bai, Jushan

Abstract

This paper studies the weak convergence of the sequential empirical process $\hat{K}_n$ 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, $\hat{K}_n$ 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.

Suggested Citation

  • Bai, Jushan, 1991. "Weak convergence of the sequential empirical processes of residuals in ARMA models," MPRA Paper 32915, University Library of Munich, Germany, revised 06 Jul 1993.
    • Handle: RePEc:pra:mprapa:32915
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    File URL: https://mpra.ub.uni-muenchen.de/32915/1/MPRA_paper_32915.pdf
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    References listed on IDEAS

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    1. J. Kreiss, 1991. "Estimation of the distribution function of noise in stationary processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 38(1), pages 285-297, December.
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    Cited by:

    1. Marc Hallin & Ramon van den Akker & Bas Werker, 2009. "A class of Simple Semiparametrically Efficient Rank-Based Unit Root Tests," Working Papers ECARES 2009_001, ULB -- Universite Libre de Bruxelles.
    2. Òscar Jordà & Alan M. Taylor, 2011. "Performance Evaluation of Zero Net-Investment Strategies," NBER Working Papers 17150, National Bureau of Economic Research, Inc.

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    More about this item

    Keywords

    Time series models; residual analysis; sequential empirical process; weak convergence; Kiefer process; change-point problem;
    All these keywords.

    JEL classification:

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

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