IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/32915.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/32915/1/MPRA_paper_32915.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zacharias Psaradakis & Marián Vávra, 2019. "Portmanteau tests for linearity of stationary time series," Econometric Reviews, Taylor & Francis Journals, vol. 38(2), pages 248-262, February.
    2. Boning Yang & Xinyi Tang & Chun Yip Yau, 2024. "Empirical prediction intervals for additive Holt–Winters methods under misspecification," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(3), pages 754-770, April.
    3. Hao Yu, 2003. "Hierarchical equilibria of branching populations," RePAd Working Paper Series lrsp-TRS391, Département des sciences administratives, UQO.
    4. Eckhard Liebscher, 1999. "Estimating the Density of the Residuals in Autoregressive Models," Statistical Inference for Stochastic Processes, Springer, vol. 2(2), pages 105-117, May.
    5. Naâmane Laïb & Mohamed Lemdani & Elias Ould‐Saïd, 2008. "On residual empirical processes of GARCH‐SM models: application to conditional symmetry tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 762-782, September.
    6. Christian Francq & Jean-Michel Zakoïan, 2020. "Adaptiveness of the empirical distribution of residuals in semi- parametric conditional location scale models," Working Papers hal-02898909, HAL.
    7. Zacharias Psaradakis & Marián Vávra, 2015. "A Quantile-based Test for Symmetry of Weakly Dependent Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 587-598, July.
    8. W. Wefelmeyer, 1994. "An efficient estimator for the expectation of a bounded function under the residual distribution of an autoregressive process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 309-315, June.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:32915. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.