On unit roots for spatial autoregressive models
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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Volume (Year): 98 (2007)
Issue (Month): 1 (January)
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References listed on IDEAS
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- 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.
- Julian Besag & Debashis Mondal, 2005. "First-order intrinsic autoregressions and the de Wijs process," Biometrika, Biometrika Trust, vol. 92(4), pages 909-920, December.
- Giacomini, Raffaella & Granger, Clive W. J., 2004.
"Aggregation of space-time processes,"
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Elsevier, vol. 118(1-2), pages 7-26.
- Raffaella Giacomini & Clive W.J. Granger, 2002. "Aggregation of Space-Time Processes," Boston College Working Papers in Economics 582, Boston College Department of Economics.
- Giacomini, Raffaella & Granger, Clive W.J., 2001. "Aggregationn of Space-Time Processes," University of California at San Diego, Economics Working Paper Series qt77f76455, Department of Economics, UC San Diego.
- 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.
- Hannes Leeb & Benedikt Poetscher, 1999. "The variance of an integrated process need not diverge to infinity," Econometrics 9907001, EconWPA.
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