IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v40y1992i2p221-243.html
   My bibliography  Save this article

Asymptotic distributions of regression and autoregression coefficients with martingale difference disturbances

Author

Listed:
  • Anderson, T. W.
  • Kunitomo, Naoto

Abstract

In this paper a form of the Lindeberg condition appropriate for martingale differences is used to obtain asymptotic normality of statistics for regression and autoregression. The regression model is yt = Bzt + vt. The unobserved error sequence {vt} is a sequence of martingale differences with conditional covariance matrices {[Sigma]t} and satisfying supt=1,..., n3{v'tvtI(v'tvt>a) zt, vt-1, zt-1, ...} 0 0 as a --> [infinity]. The sample covariance of the independent variables z1, ..., zn, is assumed to have a probability limit M, constant and nonsingular; maxt=1,...,nz'tzt/n0 0. If (1/n)[Sigma]t=1n[Sigma]t0[Sigma], constant, then [radical sign]nvec(Bn-B)0N(0,M-1[circle times operator][Sigma]) and [Sigma]n0[Sigma]. The autoregression model is xt = Bxt - 1 + vt with the maximum absolute value of the characteristic roots of B less than one, the above conditions on {vt}, and (1/n)[Sigma]t=max(r,s)+1([Sigma]t[circle times operator]vt-1-rv't-1-s)0 [delta]rs([Sigma][circle times operator][Sigma]), where [delta]rs is the Kronecker delta. Then [radical sign]nvec(Bn-B)0N(0,[Gamma]-1[circle times operator][Sigma]), where [Gamma] = [Sigma]s = 0[infinity]Bs[Sigma](B')s.

Suggested Citation

  • Anderson, T. W. & Kunitomo, Naoto, 1992. "Asymptotic distributions of regression and autoregression coefficients with martingale difference disturbances," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 221-243, February.
  • Handle: RePEc:eee:jmvana:v:40:y:1992:i:2:p:221-243
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(92)90024-A
    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.

    Citations

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


    Cited by:

    1. Svetlana Borovkova & Hendrik P. LopuhaƤ & Budi Nurani Ruchjana, 2008. "Consistency and asymptotic normality of least squares estimators in generalized STAR models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(4), pages 482-508.
    2. Anderson, T.W. & Kunitomo, Naoto & Matsushita, Yukitoshi, 2010. "On the asymptotic optimality of the LIML estimator with possibly many instruments," Journal of Econometrics, Elsevier, vol. 157(2), pages 191-204, August.
    3. Zhiyong Chen & Haibin Wang & Xuejun Wang, 2016. "The consistency for the estimator of nonparametric regression model based on martingale difference errors," Statistical Papers, Springer, vol. 57(2), pages 451-469, April.
    4. Kunitomo, Naoto & Sato, Seisho, 1996. "Asymmetry in economic time series and the simultaneous switching autoregressive model," Structural Change and Economic Dynamics, Elsevier, vol. 7(1), pages 1-34, March.
    5. Mynbaev, Kairat, 2003. "Asymptotic properties of OLS estimates in autoregressions with bounded or slowly growing deterministic trends," MPRA Paper 18448, University Library of Munich, Germany, revised 2005.

    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:40:y:1992:i:2:p:221-243. 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.

    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.