IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v107y2012icp282-305.html
   My bibliography  Save this article

Parameter estimation in a spatial unilateral unit root autoregressive model

Author

Listed:
  • Baran, Sándor
  • Pap, Gyula

Abstract

Spatial unilateral autoregressive model Xk,ℓ=αXk−1,ℓ+βXk,ℓ−1+γXk−1,ℓ−1+εk,ℓ is investigated in the unit root case, that is when the parameters are on the boundary of the domain of stability that forms a tetrahedron with vertices (1,1,−1), (1,−1,1), (−1,1,1) and (−1,−1,−1). It is shown that the limiting distribution of the least squares estimator of the parameters is normal and the rate of convergence is n when the parameters are in the faces or on the edges of the tetrahedron, while on the vertices the rate is n3/2.

Suggested Citation

  • Baran, Sándor & Pap, Gyula, 2012. "Parameter estimation in a spatial unilateral unit root autoregressive model," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 282-305.
    • Handle: RePEc:eee:jmvana:v:107:y:2012:i:c:p:282-305
    DOI: 10.1016/j.jmva.2012.01.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12000231
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2012.01.022?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Baran, Sándor & Pap, Gyula, 2009. "On the least squares estimator in a nearly unstable sequence of stationary spatial AR models," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 686-698, April.
    2. Youri Davydov & Vygantas Paulauskas, 2008. "On estimation of parameters for spatial autoregressive model," Statistical Inference for Stochastic Processes, Springer, vol. 11(3), pages 237-247, October.
    3. Paulauskas, Vygantas, 2007. "On unit roots for spatial autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 209-226, January.
    4. Baran, Sándor & Pap, Gyula & van Zuijlen, Martien C. A., 2004. "Asymptotic inference for a nearly unstable sequence of stationary spatial AR models," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 53-61, August.
    5. Bhattacharyya, B.B. & Khalil, T.M. & Richardson, G.D., 1996. "Gauss-Newton estimation of parameters for a spatial autoregression model," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 173-179, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Baran, Sándor & Pap, Gyula, 2009. "On the least squares estimator in a nearly unstable sequence of stationary spatial AR models," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 686-698, April.
    2. Martellosio, Federico, 2011. "Efficiency of the OLS estimator in the vicinity of a spatial unit root," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1285-1291, August.
    3. Martellosio, Federico, 2008. "Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression," MPRA Paper 7255, University Library of Munich, Germany.
    4. B. Bhattacharyya & X. Li & M. Pensky & G. Richardson, 2000. "Testing for Unit Roots in a Nearly Nonstationary Spatial Autoregressive Process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(1), pages 71-83, March.
    5. Ojeda, Silvia & Vallejos, Ronny & Bustos, Oscar, 2010. "A new image segmentation algorithm with applications to image inpainting," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2082-2093, September.
    6. Grisel Maribel Britos & Silvia María Ojeda, 2019. "Robust estimation for spatial autoregressive processes based on bounded innovation propagation representations," Computational Statistics, Springer, vol. 34(3), pages 1315-1335, September.

    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:107:y:2012:i:c:p:282-305. 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.

    If CitEc recognized a bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.