Abstract
Let be a zero mean weakly stationary random field and consider the problem of predicting X(0, 0) based on the incomplete quarter-plane past. An explicit formula is obtained for the prediction error of a future value of weakly stationary random fields when the quarter-plane
is altered by some missing observations. Some properties for autoregressive (AR) random fields and for moving average (MA) are established.
Acknowledgement
We would like to thank the anonymous reviewers and associate editor for their valuable suggestions and helpful remarks that improved the quality and the presentation of the paper.