Benchmarking Systems of Seasonally Adjusted Time Series

When a system of time series is seasonally adjusted, generally the accounting constraints originally linking the series are not fulfilled. To overcome this problem, we discuss an extension to a system of series linked by an accounting constraint of the classical univariate benchmarking procedure due to Denton (1971), which is founded on a movement preservation principle that is very relevant in this case. The presence of linear dependence between the variables makes it necessary to deal with the whole set of contemporaneous and temporal aggregation relationships. The cases of one-way classified (e.g., by regions or by industries) and of two-way classified (e.g., by regions and by industries) systems of series are studied. An empirical application to the Canadian retail trade series by province (12 series) and trade groups (18 series) is considered to show the capability of the proposed procedures.