Qiwei Yao, London School of Economics
Peter J. Brockwell, Colorado State University
Abstract
This paper examines the Gaussian maximum likelihood estimator (GMLE) in the context of a general form of spatial ARMA processes with finite second moment. The ARMA processes are supposed to be causal and invertible under the half-plane unilateral order (Whittle 1954), but not necessarily Gaussian. We show that the GMLE is consistent. Subject to a modification to confine the edge effect, it is also asymptotically distribution-free in the sense that the limit distribution is normal, unbiased and with a variance depending on the autocorrelation function only. This is an analogue of Hannan's classic result for time series in the context of spatial processes; see Theorem 10.8.2 of Brockwell and Davis (1991). We also point out that the computation of the GMLE can be easily implemented on an average PC via the prewhitening based on the innovation algorithm, which in fact is widely applicable to any lattice or non-lattice processes.