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X-13ARIMA-SEATS Seasonal Adjustment Program

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Comparison of X-12-ARIMA Trading Day and Holiday Regressors With Country Specific Regressors

Christopher G. Roberts(1), Scott H. Holan(2), and Brian C. Monsell(3)


Several methods exist which can adjust for trading day and holiday effects in monthly economic time series. This paper reviews and compares two such methodologies for conducting proper adjustments. The two methodologies are based upon the U.S. Census Bureau's X-12-ARIMA method and one developed by the Statistical Offices of the European Communities, commonly referred to as Eurostat. Three different methods are used to compare the U.S. Census Bureau procedure and the Eurostat-inspired procedure. These methods are spectral analysis, sample-size corrected AIC comparisons, and examination of out-of-sample forecast errors. Finally, these comparisons are conducted using nearly 100 U.S. Census Bureau time series of manufacturing data, retail sales, and housing starts. This empirical study is the first of its kind and therefore provides an important contribution to the seasonal adjustment community.


Eurostat; Holiday effect; Model selection; RegARIMA model; Trading day effect; X-12-ARIMA.

(1) Christopher Roberts currently works for Ernst and Young.

(2) Scott Holan is a professor in the Department of Statistics, University of Missouri-Columbia.

(3) Brian C. Monsell is Mathematical Statistican, Center for Statistical Research and Methodology U. S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email :

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Source: U.S. Census Bureau | Center for Statistical Research and Methodology | (301) 763-1649 (or |  Last Revised: August 07, 2015