The estimation of M disaggregate time series when contemporaneous and temporal aggregates are known

We discuss the problem of estimating M ( > 1) high-frequency (say, quarterly or monthly) time series using the relevant low-frequency (say, annual or quarterly) data, the sum for each intra-annual period of the series to be estimated and, finally, a number of related indicators. The optimal (in least squares sense) estimator that fulfills both temporal and contemporaneous aggregation constraints is derived. In addition, we critically comment on the estimation approach followed by Rossi (1982), showing that a convenient reformulation of that method can be viewed as a special application of a known adjustment technique.