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Parameter estimation in a spatial unilateral unit root autoregressive model

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  • 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
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    References listed on IDEAS

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    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. 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.
    4. 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.
    5. Paulauskas, Vygantas, 2007. "On unit roots for spatial autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 209-226, January.
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    Cited by:

    1. Badi H. Baltagi & Junjie Shu, 2024. "A Survey of Spatial Unit Roots," Mathematics, MDPI, vol. 12(7), pages 1-31, March.

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