Advanced Search
MyIDEAS: Login to save this article or follow this journal

Gauss-Newton and M-estimation for ARMA processes with infinite variance


Author Info

  • Davis, Richard A.
Registered author(s):


    We consider two estimation procedures, Gauss-Newton and M-estimation, for the parameters of an ARMA (p,q) process when the innovations belong to the domain of attraction of a nonnormal stable distribution. The Gauss-Newton or iterative least squares estimate is shown to have the same limiting distribution as the maximum likelihood and Whittle estimates. The latter was derived recently by Mikosch et al. (1995). We also establish the weak convergence for a class of M-estimates, including the case of least absolute deviation, and show that, asymptotically, the M-estimate dominates both the Gauss-Newton and Whittle estimates. A brief simulation is carried out comparing the performance of M-estimation with iterative and ordinary least squares. As suggested by the asymptotic theory, M-estimation, using least absolute deviation for the loss function, outperforms the other two procedures.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 63 (1996)
    Issue (Month): 1 (October)
    Pages: 75-95

    as in new window
    Handle: RePEc:eee:spapps:v:63:y:1996:i:1:p:75-95

    Contact details of provider:
    Web page:

    Order Information:
    Postal: http://

    Related research

    Keywords: Gauss-Newton estimate Heavy-tails Stable distributions M-estimation ARMA processes;


    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Kl├╝ppelberg, Claudia & Mikosch, Thomas, 1993. "Spectral estimates and stable processes," Stochastic Processes and their Applications, Elsevier, vol. 47(2), pages 323-344, September.
    2. Davis, Richard A. & Knight, Keith & Liu, Jian, 1992. "M-estimation for autoregressions with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 145-180, February.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:
    1. Li, Jinyu & Liang, Wei & He, Shuyuan, 2011. "Empirical likelihood for LAD estimators in infinite variance ARMA models," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 212-219, February.
    2. SBRANA, Giacomo & SILVESTRINI, Andrea, 2010. "Aggregation of exponential smoothing processes with an application to portfolio risk evaluation," CORE Discussion Papers 2010039, Universit├ę catholique de Louvain, Center for Operations Research and Econometrics (CORE).


    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


    Access and download statistics


    When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:63:y:1996:i:1:p:75-95. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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