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

The relationship between the discrete time nearly unit root doubly geometric spatial model and the continuous time Ornstein-Uhlenbeck random field is investigated. It turns out that the Ornstein-Uhlenbeck sheet can be considered as the continuous time counterpart of the doubly geometric model. However, it is shown that in contrast to the one-dimensional case and due to the orthogonality of the measures generated by the Ornstein-Unlenbeck sheets with different parameters, this connection does not hold on the level of estimators.