Some Inference Results for Causal Autoregressive Processes on a Plane

We investigate the causal autoregressive process on a plane pioneered by Whittle (On stationary processes on the plane. Biometrika 41 (1954), 434–49) and further studied by Besag (Spatial interaction and statistical analysis of lattice systems. J. R. Stat. Soc. Ser. B 36 (1974), 192–236). We develop test statistics to test composite hypotheses about the parameters and to test if the process is separable. Also, when some data points are missing, we develop a computational procedure obtained by combining the EM algorithm and bootstrap procedures to find estimates of the parameters and hence the distribution of these estimates.