IDEAS home Printed from https://ideas.repec.org/a/ecm/emetrp/v58y1990i1p145-63.html
   My bibliography  Save this article

A General Approach to the Limiting Distribution for Estimators in Time Series Regression with Nonstable Autoregressive Errors

Author

Listed:
  • Nabeya, Seiji
  • Tanaka, Katsuto

Abstract

The authors consider the time series regression model where the error term follows a nonstable autoregressive process and present a general approach for delivering the limiting distribution of a normalized estimator for the autoregressive parameter. The present approach is quite straightforward and leads them to an accurate evaluation of the distribution function, unlike the other approaches suggested in the literature. The authors' methodology is illustrated and percent points are tabulated. The present approach produces a good approximation method for the finite sample distribution and also provides an accurate evaluation of the limiting powers of some unit root tests under a sequence of local alternatives. Copyright 1990 by The Econometric Society.

Suggested Citation

  • Nabeya, Seiji & Tanaka, Katsuto, 1990. "A General Approach to the Limiting Distribution for Estimators in Time Series Regression with Nonstable Autoregressive Errors," Econometrica, Econometric Society, vol. 58(1), pages 145-163, January.
    • Handle: RePEc:ecm:emetrp:v:58:y:1990:i:1:p:145-63
    as

    Download full text from publisher

    File URL: http://links.jstor.org/sici?sici=0012-9682%28199001%2958%3A1%3C145%3AAGATTL%3E2.0.CO%3B2-4&origin=repec
    File Function: full text
    Download Restriction: Access to full text is restricted to JSTOR subscribers. See http://www.jstor.org for details.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

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


    Cited by:

    1. Ren, Yu & Tu, Yundong & Yi, Yanping, 2019. "Balanced predictive regressions," Journal of Empirical Finance, Elsevier, vol. 54(C), pages 118-142.
    2. Tanaka, Katsuto & 田中, 勝人, 2011. "Distributions of Quadratic Functionals of the Fractional Brownian Motion Based on a Martingale Approximation," Discussion Papers 2011-06, Graduate School of Economics, Hitotsubashi University.
    3. Paparoditis, Efstathios & Politis, Dimitris N, 2013. "The Asymptotic Size and Power of the Augmented Dickey-Fuller Test for a Unit Root," University of California at San Diego, Economics Working Paper Series qt0784p55m, Department of Economics, UC San Diego.
    4. Mukhtar Ali, 2002. "Distribution Of The Least Squares Estimator In A First-Order Autoregressive Model," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 89-119.
    5. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December.
    6. Zhongwen Liang, 2017. "A Unified Approach on the Local Power of Panel Unit Root Tests," Papers 1710.02944, arXiv.org.
    7. MacKinnon, James G, 1994. "Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 167-176, April.
    8. Elliott, Graham & Stock, James H., 1994. "Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 672-700, August.
    9. Mukhtar M. Ali, 1996. "Distribution of the Least Squares Estimator in a First-Order Autoregressive Model," Econometrics 9610004, University Library of Munich, Germany.
    10. Perron, Pierre, 1996. "The adequacy of asymptotic approximations in the near-integrated autoregressive model with dependent errors," Journal of Econometrics, Elsevier, vol. 70(2), pages 317-350, February.
    11. Mehdi Hosseinkouchack, 2014. "Local Asymptotic Power of Breitung's Test," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(3), pages 456-462, June.
    12. HORIE, Tetsushi & 堀江, 哲史 & YAMAMOTO, Yohei & 山本, 庸平, 2016. "Testing for Speculative Bubbles in Large-Dimensional Financial Panel Data Sets," Discussion Papers 2016-04, Graduate School of Economics, Hitotsubashi University.
    13. Ulrich K. Müller, 2002. "Size and Power of Tests for Stationarity in Highly Autocorrelated Time Series," University of St. Gallen Department of Economics working paper series 2002 2002-26, Department of Economics, University of St. Gallen.
    14. Muller, Ulrich K., 2005. "Size and power of tests of stationarity in highly autocorrelated time series," Journal of Econometrics, Elsevier, vol. 128(2), pages 195-213, October.
    15. María Presno & Anna López, 2003. "Testing for stationarity in series with a shift in the mean. A fredholm approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 195-213, June.

    More about this item

    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:ecm:emetrp:v:58:y:1990:i:1:p:145-63. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.