Linear Approximations to the Census and BLS Seasonal Adjustment Methods

The Census and BLS ratio-to-moving-average seasonal adjustment methods are usually specified by procedural steps. They can be written mathematically as combinations of linear and non-linear operations on the logarithms of the original series. For some purposes the non-linear operations can be ignored. The Census and BLS historical seasonal factors are almost identical to those from a simpler model using ratios to a centered 12-term moving average. They also closely resemble those from regression models using seven years of data. In three test series, revisions between current seasonal factors and historical seasonal factors obtained when the adjustment is recomputed with additional data are smaller with the Census model than with the 12-term or regression models. By recomputing the adjustment twice a year instead of once, the same size revisions are obtained with the 12-term as with the Census model. The Census trend-cycle specifications differ from the 12-term and regression models.