IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v99y2008i1p25-49.html
   My bibliography  Save this article

Approximating posterior probabilities in a linear model with possibly noninvertible moving average errors

Author

Listed:
  • Pokta, Suriani
  • Hart, Jeffrey D.

Abstract

The method of Laplace is used to approximate posterior probabilities for a collection of polynomial regression models when the errors follow a process with a noninvertible moving average component. These results are useful in the problem of period-change analysis of variable stars and in assessing the posterior probability that a time series with trend has been overdifferenced. The nonstandard covariance structure induced by a noninvertible moving average process can invalidate the standard Laplace method. A number of analytical tools is used to produce corrected Laplace approximations. These tools include viewing the covariance matrix of the observations as tending to a differential operator. The use of such an operator and its Green's function provides a convenient and systematic method of asymptotically inverting the covariance matrix. In certain cases there are two different Laplace approximations, and the appropriate one to use depends upon unknown parameters. This problem is dealt with by using a weighted geometric mean of the candidate approximations, where the weights are completely data-based and such that, asymptotically, the correct approximation is used. The new methodology is applied to an analysis of the prototypical long-period variable star known as Mira.

Suggested Citation

  • Pokta, Suriani & Hart, Jeffrey D., 2008. "Approximating posterior probabilities in a linear model with possibly noninvertible moving average errors," Journal of Multivariate Analysis, Elsevier, vol. 99(1), pages 25-49, January.
  • Handle: RePEc:eee:jmvana:v:99:y:2008:i:1:p:25-49
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(07)00058-9
    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.

    References listed on IDEAS

    as
    1. Tsay, Ruey S, 1993. "Testing for Noninvertible Models with Applications," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 225-233, April.
    2. Sargan, J D & Bhargava, Alok, 1983. "Maximum Likelihood Estimation of Regression Models with First Order Moving Average Errors When the Root Lies on the Unit Circle," Econometrica, Econometric Society, vol. 51(3), pages 799-820, May.
    3. Plosser, Charles I. & Schwert, G. William, 1977. "Estimation of a non-invertible moving average process : The case of overdifferencing," Journal of Econometrics, Elsevier, vol. 6(2), pages 199-224, September.
    Full references (including those not matched with items on IDEAS)

    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:jmvana:v:99:y:2008:i:1:p:25-49. 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: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.