IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v32y1997i4p405-411.html
   My bibliography  Save this article

A note on the residual empirical process in autoregressive models

Author

Listed:
  • Lee, Sangyeol

Abstract

Suppose that {Xt} is the stationary AR(p) process of the form: Xt - [mu] = [beta]1(Xt-1 - [mu]) + ... + [beta]p(Xt-p - [mu]) + [var epsilon]t, where {[var epsilon]t} is a sequence of i.i.d. random variables with mean zero and finite variance [sigma]2. In this paper, we study the asymptotic behavior of the empirical process computed from the least-squares residuals, for which some estimators of [mu] and [sigma]2 are substituted. Due to the estimation of the location and scale parameters, the limiting process of the residual empirical process is shown to be a Gaussian process which is not a standard Brownian bridge. The result is applicable to the goodness-of-fit test of the errors in autoregressive processes.

Suggested Citation

  • Lee, Sangyeol, 1997. "A note on the residual empirical process in autoregressive models," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 405-411, April.
    • Handle: RePEc:eee:stapro:v:32:y:1997:i:4:p:405-411
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(96)00100-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

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


    Cited by:

    1. Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2016. "Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 582-594.
    2. Bouhaddioui, Chafik & Ghoudi, Kilani, 2012. "Empirical processes for infinite variance autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 319-335.

    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:eee:stapro:v:32:y:1997:i:4:p:405-411. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.