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X-13ARIMA-SEATS Seasonal Adjustment Program

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Comparing Automatic Modeling Procedures of TRAMO and X-12-ARIMA, an Update

Kathleen M. McDonald-Johnson(1), Catherine C. Harvill Hood,(2), Brian C. Monsell(3), Chak Li(4)


The U. S. Census Bureau's enhanced X-12-ARIMA seasonal adjustment program includes the automatic ARIMA (Autoregressive Integrated Moving Average) model selection procedure developed by Statistics Canada and a second procedure based on the automatic procedure of TRAMO (Time series Regression with ARIMA noise, Missing observations and Outliers), a modeling package developed by Victor Gómez and Agustín Maravall. Each program has automatic identification of key regressors, allowing for full automatic selection of a regARIMA model (regression with an underlying ARIMA process). X-12-ARIMA's procedure differs from TRAMO's in a number of ways. Our study updates previous work as we compared the procedures again using improved versions of the two programs. We applied the procedures to a set of Census Bureau time series and simulations. When model choices differed, we compared standard modeling diagnostics to look for a consistent preference for either procedure. As in the previous study, we found that X-12-ARIMA still seems to choose trading day effects more appropriately than TRAMO. However, we found that X-12-ARIMA inaccurately identifies Easter effects more often than TRAMO. Overall, we found that the diagnostics for the X-12-ARIMA models were at least as good as the diagnostics from TRAMO models.


Time series, Seasonal adjustment, Trading day effect

(1) Kathleen M. McDonald-Johnson is Mathematical Statistican, Office of Statistical Methods and Research for Economic Programs, U. S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email :

(2) Catherine C. H. Hood is currently a consultant. email :

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

(4) Chak Li was a student intern at the Census Bureau.

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Source: U.S. Census Bureau | Center for Statistical Research and Methodology | (301) 763-1649 (or |  Last Revised: April 02, 2015