IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Asymptotic Efficiency of the OLS Estimator with Singular Limiting Sample Moment Matrices

  • Yoshimasa Uematsu
Registered author(s):

    This paper presents a time series model that has an asymptotically efficient ordinary least squares (OLS) estimator, irrespective of the singularity of its limiting sample moment matrices. In the literature on stationary time series analysis, Grenander and Rosenblatt's (1957) (G-R) classical result is used to judge the asymptotic efficiency of regression coefficients on deterministic regressors satisfying Grenander's condition. Without this condition, however, it is not obvious that the model is efficient. In this paper, we introduce such a model by proving the efficiency of the model with a slowly varying (SV) regressor under the same condition on error terms constrained in G-R. This kind of regressor is known to display asymptotic singularity in the sample moment matrices, as in Phillips (2007), such that Grenander's condition fails.

    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: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd11-208.pdf
    Download Restriction: no

    Paper provided by Institute of Economic Research, Hitotsubashi University in its series Global COE Hi-Stat Discussion Paper Series with number gd11-208.

    as
    in new window

    Length:
    Date of creation: Oct 2011
    Date of revision:
    Handle: RePEc:hst:ghsdps:gd11-208
    Contact details of provider: Postal: 2-1 Naka, Kunitachi City, Tokyo 186
    Phone: +81-42-580-8327
    Fax: +81-42-580-8333
    Web page: http://www.ier.hit-u.ac.jp/Email:


    More information through EDIRC

    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. Pierre Perron & Tomoyoshi Yabu, 2005. "Estimating Deterministric Trends with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2005-037, Boston University - Department of Economics.
    2. Mynbaev, Kairat T., 2009. "Central Limit Theorems For Weighted Sums Of Linear Processes: Lp -Approximability Versus Brownian Motion," Econometric Theory, Cambridge University Press, vol. 25(03), pages 748-763, June.
    3. Shin, Dong Wan & Oh, Man Suk, 2002. "Asymptotic Efficiency Of The Ordinary Least Squares Estimator For Regressions With Unstable Regressors," Econometric Theory, Cambridge University Press, vol. 18(05), pages 1121-1138, October.
    4. Phillips, Peter C.B., 2007. "Regression With Slowly Varying Regressors And Nonlinear Trends," Econometric Theory, Cambridge University Press, vol. 23(04), pages 557-614, August.
    5. Kramer, Walter & Hassler, Uwe, 1998. "Limiting efficiency of OLS vs. GLS when regressors are fractionally integrated," Economics Letters, Elsevier, vol. 60(3), pages 285-290, September.
    6. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
    Full references (including those not matched with items on IDEAS)

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

    When requesting a correction, please mention this item's handle: RePEc:hst:ghsdps:gd11-208. 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: (Tatsuji Makino)

    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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.