Abstract

The vast majority of time series data produced by a statistical agency are part of a system of time series classified by attributes. The series of such systems must satisfy cross-sectional (contemporaneous) aggregation constraints. This requires that the values of the component elementary series add up to marginal totals for each period of time. In some cases, each series must also add up to temporal benchmarks and therefore, must satisfy temporal aggregation constraints. Many time series processes such as seasonal adjustment are nonlinear and will destroy the linear relationships of the system. ^* Other processes such as those related to the combination of various sources of data and forecasting can also produce series that will fail to meet the aggregation constraints. To restore the coherence of the set of series, temporal benchmarking, reconciliation, or balancing processes must be applied.