Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization

This article considers the problem of adjusting monthly or quarterly time series to make them accord with independent annual totals or averages without introducing artificial discontinuities. A general approach and some specific procedures involving constrained minimization of a quadratic form in the differences between revised and unrevised series are proposed. Some computational advantages are noted. Attention is given to the relationships between the adjustment problem and earlier work by other authors on the creation of monthly or quarterly series when only annual figures are available. An example is provided to illustrate the application of the proposed adjustment procedures.