Prediction in the serially correlated error component model. For the BLU predictor of \(y_{i, T+1}\) given in (5.25), show that when \(v_{i t}\) follows

(a) the AR(1) process, the GLS predictor is corrected by the term in (5.26);

(b) the AR(2) process, the GLS predictor is corrected by the term given in (5.27);

(c) the specialized AR(4) process, the GLS predictor is corrected by the term given in (5.28);

(d) the MA(1) process, the GLS predictor is corrected by the term given in (5.29).

i.T+1 = ZT+18GLS + w'uGLS (5.25)