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On unit roots for spatial autoregressive models

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  • Paulauskas, Vygantas
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    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.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 1 (January)
    Pages: 209-226

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:1:p:209-226
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    1. Leeb, Hannes & P tscher, 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(04), pages 671-685, August.
    2. Giacomini, Raffaella & Granger, Clive W. J., 2004. "Aggregation of space-time processes," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 7-26.
    3. Julian Besag & Debashis Mondal, 2005. "First-order intrinsic autoregressions and the de Wijs process," Biometrika, Biometrika Trust, vol. 92(4), pages 909-920, December.
    4. Hannes Leeb & Benedikt Poetscher, 1999. "The variance of an integrated process need not diverge to infinity," Econometrics 9907001, EconWPA.
    5. 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.
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