A note on the exact transformation associated with the first-order moving average process

Exact analytical expressions for the transformation that can be used to transform a generalized regression problem into a simple regression problem are available for a variety of models. Such is the case, for instance, for purely heteroscedastic models, for the first-order Markov process and for error components models. For the first-order moving average process, on the other hand, the exact transformation has not yet been produced. This gap is filled in the present note.Implications for estimation and prediction are also considered.