Least-squares reconciliation of large systems of sub-annual time series. A comparison of alternative solutions.

A system of sub-annual time series (say, quarterly) is generally required to be coherent with known totals. Usually, such constraints are contemporaneous, when the variables of the system are subject to one or more accounting relationships in every period; temporal, when high-frequency series are to be consistent with known (more reliable) low-frequency counterparts (say, annual). However, some inconsistencies are likely to appear in the system when variables are estimated independently. Restoring the fullfilment of both contemporaneous and temporal constraints represents the problem of reconciliation.