IDEAS home Printed from https://ideas.repec.org/a/ect/emjrnl/v5y2002i2p387-416.html
   My bibliography  Save this article

Testing for reduction to random walk in autoregressive conditional heteroskedasticity models

Author

Listed:
  • Claudia Klüppelberg
  • Ross A. Maller
  • Mark van de Vyver
  • Derick Wee

Abstract

The autoregressive--ARCH (AR--ARCH) and autoregressive--GARCH (AR--GARCH) models, which allow for conditional heteroskedasticity and autoregression, reduce to random walk or white noise for some values of the parameters. We consider generalized versions of the AR--ARCH(1) and AR--GARCH(1,1) models, and, under mild assumptions, calculate the asymptotic distributions of pseudo-likelihood ratio statistics for testing hypotheses that reflect these reductions. These hypotheses are of two kinds: the conditional volatility parameters may take their boundary values of zero, or the autoregressive component may take the form of a unit root process or not in fact be present. The limiting distributions of the resulting test statistics can be expressed in terms of functionals of Brownian motion related to the Dickey--Fuller statistic, together with independent chi-square components. The finite sample performances of the test statistics are assessed by simulations, and percentiles are tabulated. The results have applications in the analysis of financial time series and random coefficient models. Copyright Royal Economic Society, 2002

Suggested Citation

  • Claudia Klüppelberg & Ross A. Maller & Mark van de Vyver & Derick Wee, 2002. "Testing for reduction to random walk in autoregressive conditional heteroskedasticity models," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 387-416, June.
    • Handle: RePEc:ect:emjrnl:v:5:y:2002:i:2:p:387-416
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

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


    Cited by:

    1. Muriel, Nelson & González-Farías, Graciela, 2018. "Testing the null of difference stationarity against the alternative of a stochastic unit root: A new test based on multivariate STUR," Econometrics and Statistics, Elsevier, vol. 7(C), pages 46-62.
    2. Giuseppe Cavaliere & Anders Rahbek, 2019. "A Primer On Bootstrap Testing Of Hypotheses In Time Series Models: With An Application To Double Autoregressive Models," Discussion Papers 19-03, University of Copenhagen. Department of Economics.
    3. Christian Francq & Jean-Michel Zakoïan, 2006. "Inference in GARCH when some coefficients are equal to zero," Computing in Economics and Finance 2006 64, Society for Computational Economics.
    4. Francq, Christian & Zakoïan, Jean-Michel, 2009. "Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 313-324.
    5. Yoon, Gawon, 2016. "Stochastic unit root processes: Maximum likelihood estimation, and new Lagrange multiplier and likelihood ratio tests," Economic Modelling, Elsevier, vol. 52(PB), pages 725-732.

    More about this item

    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:ect:emjrnl:v:5:y:2002:i:2:p:387-416. 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: Wiley-Blackwell Digital Licensing or Christopher F. Baum (email available below). General contact details of provider: https://edirc.repec.org/data/resssea.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.