The problem of decomposing an observed series, assumed to follow an ARIMA process, into signal plus noise is considered. It is well known that the preliminary estimates of the signal will be subject to revisions as more data become available. For a general ARIMA process, the revision in the concurrent estimate of the signal is seen to follow a stationary ARMA process, easily derived from the overall series model. The results are extended to non-concurrent preliminary estimates. Finally, it is found that, except for a scale factor, the revisions are the same for all admissible decompositions and the canonical decomposition maximizes the variance of the revision.