On linear prediction for stationary random fields with nonsymmetrical half-plane past

An explicit autoregressive series representation for the best multi-step ahead linear predictor of stationary random fields with nonsymmetrical half-plane past (NSHP) is established. Necessary and sufficient condition for the mean square convergence of these series is given. Moreover, step recursive relations between the prediction coefficients for the infinite past predictor are provided, these relations are used to calculate explicitly the multi-step prediction coefficients. Some specific examples to validate the applicability of our relations are presented.