Prediction of random fields with incomplete quarter-plane past

Abdelghani Hamaz

Communications in Statistics - Theory and Methods, 2019, vol. 48, issue 11, 2707-2716

Abstract: Let {X(n,m);(n,m)∈Z2} 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 Q={(n,m)∈Z2;n≤0,m≤0,(n,m)≠(0,0)} is altered by some missing observations. Some properties for autoregressive (AR) random fields and for moving average (MA) are established.

Date: 2019
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DOI: 10.1080/03610926.2018.1472789

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