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On unit roots for spatial autoregressive models

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  • Paulauskas, Vygantas

Abstract

In this paper we consider the unit root problem for one rather simple autoregressive model Yt,s=aYt-1,s+bYt,s-1+[var epsilon]t,s on a two-dimensional lattice. We show that the growth of variance of Yt,s is essentially different from corresponding growth in the unit root case for AR(1) or AR(2) time series models. We also show that the dimension of the lattice plays an important role: the growth of variance of autoregressive field on a d-dimensional lattice is different for d=2,3 and d>=4.

Suggested Citation

  • Paulauskas, Vygantas, 2007. "On unit roots for spatial autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 209-226, January.
    • Handle: RePEc:eee:jmvana:v:98:y:2007:i:1:p:209-226
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    References listed on IDEAS

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    1. Hannes Leeb & Benedikt Poetscher, 1999. "The variance of an integrated process need not diverge to infinity," Econometrics 9907001, University Library of Munich, Germany.
    2. Bhattacharyya, B. B. & Ren, J. -J. & Richardson, G. D. & Zhang, J., 2003. "Spatial autoregression model: strong consistency," Statistics & Probability Letters, Elsevier, vol. 65(2), pages 71-77, November.
    3. Giacomini, Raffaella & Granger, Clive W. J., 2004. "Aggregation of space-time processes," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 7-26.
    4. Leeb, Hannes & Pötscher, Benedikt M., 2001. "The Variance Of An Integrated Process Need Not Diverge To Infinity, And Related Results On Partial Sums Of Stationary Processes," Econometric Theory, Cambridge University Press, vol. 17(4), pages 671-685, August.
    5. Julian Besag & Debashis Mondal, 2005. "First-order intrinsic autoregressions and the de Wijs process," Biometrika, Biometrika Trust, vol. 92(4), pages 909-920, December.
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    Cited by:

    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. Badi H. Baltagi & Junjie Shu, 2024. "A Survey of Spatial Unit Roots," Mathematics, MDPI, vol. 12(7), pages 1-32, March.
    3. 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.
    4. 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.
    5. Martellosio, Federico, 2008. "Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression," MPRA Paper 7255, University Library of Munich, Germany.

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