An empirical comparison of methods for benchmarking seasonally adjusted series to annual totals

For benchmarking monthly and quarterly series to annual series and to the Economic Census every five years, the U.S. Census Bureau uses an iterative, nonlinear method known as the Causey-Trager method. However, the Census Bureau's X−12−ARIMA seasonal adjustment program uses a modified Denton procedure to benchmark the seasonally adjusted series to the annual totals of the unadjusted series that can result in distortions in the benchmarked seasonally adjusted series. Some users have requested a different benchmark method in X−12−ARIMA. Statistics Canada has proposed several different benchmark methods, including a regression procedure, to replace the modified Denton method for benchmarking in X−12−ARIMA. Using a sample of U.S. time series, this paper investigates the properties of the benchmarks from the current procedure in X−12−ARIMA, the new methods proposed by Statistics Canada, and the Causey-Trager method for benchmarking the seasonally adjusted series to the annual totals of the raw data. The objective of this study is two-fold: 1) to look at some of the properties of the various benchmarking procedures under consideration at the Census Bureau and Statistics Canada for benchmarking seasonally adjusted series, and 2) to look at possible settings for the regression procedure from Statistics Canada. There were very consistent results with smooth benchmark factors and small discrepancies in the month-to-month changes with both the Causey-Trager method and the Regression method with λ = 1.