IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1361.html
   My bibliography  Save this paper

Valid Edgeworth Expansions for the Whittle Maximum Likelihood Estimator for Stationary Long-memory Gaussian Time Series

Author

Listed:
  • Donald W.K. Andrews

    () (Cowles Foundation)

  • Offer Lieberman

    (Technion-Israel Institute of Technology)

Abstract

In this paper, we prove the validity of an Edgeworth expansion to the distribution of the Whittle maximum likelihood estimator for stationary long-memory Gaussian models with unknown parameter theta in Theta subset R^{d_{theta}} . The error of the (s-2)-order expansion is shown to be o(n^{(s-2)/2}) -- the usual iid rate -- for a wide range of models, including the popular ARFIMA(p,d,q) models. The expansion is valid under mild assumptions on the behavior of spectral density and its derivatives in the neighborhood of the origin. As a by-product, we generalize a Theorem by Fox and Taqqu (1987) concerning the asymptotic behavior of Toeplitz matrices. Lieberman, Rousseau, and Zucker (2002) (LRZ) establish a valid Edgeworth expansion for the maximum likelihood estimator for stationary long-memory Gaussian models. For a significant class of models, their expansion is shown to have an error of o(n-1). The results given here improve upon those of LRZ in that the results provide an Edgeworth expansion for an asymptotically efficient estimator, as LRZ do, but the error of the expansion is shown to be o(n^{-(s-2)/2}), not o(n^{-1}), for a broad range of models.

Suggested Citation

  • Donald W.K. Andrews & Offer Lieberman, 2002. "Valid Edgeworth Expansions for the Whittle Maximum Likelihood Estimator for Stationary Long-memory Gaussian Time Series," Cowles Foundation Discussion Papers 1361, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1361
    Note: CFP 1162.
    as

    Download full text from publisher

    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d13/d1361.pdf
    Download Restriction: no

    Other versions of this item:

    Citations

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


    Cited by:

    1. Morten ├śrregaard Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 405-443.
    2. repec:bpj:jecome:v:7:y:2018:i:1:p:38:n:2 is not listed on IDEAS
    3. Stelios Arvanitis & Antonis Demos, "undated". "A Class of Indirect Inference Estimators: Higher Order Asymptotics and Approximate Bias Correction (Revised)," DEOS Working Papers 1411, Athens University of Economics and Business, revised 23 Sep 2014.
    4. Arvanitis Stelios & Demos Antonis, 2018. "On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Inference Estimators," Journal of Econometric Methods, De Gruyter, vol. 7(1), pages 1-38, January.
    5. Andrews, Donald W.K. & Lieberman, Offer & Marmer, Vadim, 2006. "Higher-order improvements of the parametric bootstrap for long-memory Gaussian processes," Journal of Econometrics, Elsevier, vol. 133(2), pages 673-702, August.
    6. Poskitt, D.S. & Grose, Simone D. & Martin, Gael M., 2015. "Higher-order improvements of the sieve bootstrap for fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 188(1), pages 94-110.

    More about this item

    Keywords

    ARFIMA; Edgeworth expansion; Long Memory; Whittle estimator;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

    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:cwl:cwldpp:1361. 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: (Matthew Regan). General contact details of provider: http://edirc.repec.org/data/cowleus.html .

    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 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.

    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.