Asymptotic inference for spatial autoregression and orthogonality of Ornstein-Uhlenbeck sheets

The relationship between the discrete time nearly unit root doubly geometri c spatial model and the continuous time Ornstein-Uhlenbeck random field is investigated. It turns out that the Ornstein-Uhlenbeck sheet can be conside red as the continuous time counterpart of the doubly geometric model. Howev er, it is shown that in contrast to the one-dimensional case and due to the orthogonality of the measures generated by the Ornstein-Uhlenbeck sheets w ith different parameters, this connection does not hold on the level of est imators. (C) 2001 Elsevier Science Ltd. All rights reserved.