IDEAS home Printed from
   My bibliography  Save this paper

Robust Estimation of ARMA Models with Near Root Cancellation


  • Cogley, Timothy
  • Startz, Richard


Standard estimation of ARMA models in which the AR and MA roots nearly cancel, so that individual coefficients are only weakly identified, often produces inferential ranges for individual coefficients that give a spurious appearance of accuracy. We remedy this problem with a model that mixes inferential ranges from the estimated model with those of a more parsimonious model. The mixing probability is derived using Bayesian methods, but we show that the method works well in both Bayesian and frequentist setups. In particular, we show that our mixture procedure weights standard results heavily when given data from a well-identified ARMA model (which does not exhibit near root cancellation) and weights heavily an uninformative inferential region when given data from a weakly-identified ARMA model (with near root cancellation). When our procedure is applied to a well-identified process the investigator gets the “usual results,†so there is no important statistical cost to using our procedure. On the other hand, when our procedure is applied to a weakly-identified process, the investigator learns that the data tell us little about the parameters—and is thus protected against making spurious inferences. We recommend that mixture models be computed routinely when inference about ARMA coefficients is of interest.

Suggested Citation

  • Cogley, Timothy & Startz, Richard, 2012. "Robust Estimation of ARMA Models with Near Root Cancellation," University of California at Santa Barbara, Economics Working Paper Series qt0cw056qz, Department of Economics, UC Santa Barbara.
  • Handle: RePEc:cdl:ucsbec:qt0cw056qz

    Download full text from publisher

    File URL:;origin=repeccitec
    Download Restriction: no

    References listed on IDEAS

    1. Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
    2. Nelson, Charles R. & Startz, Richard, 2007. "The zero-information-limit condition and spurious inference in weakly identified models," Journal of Econometrics, Elsevier, vol. 138(1), pages 47-62, May.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Social and Behavioral Sciences; ARMA; bayesian; weak identification;

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:cdl:ucsbec:qt0cw056qz. 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: (Lisa Schiff). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.