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X-13ARIMA-SEATS Seasonal Adjustment Program

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Improving the Automatic RegARIMA Model Selection Procedures of X-12-ARIMA Version 0.3

by Kathleen M. McDonald-Johnson (1), Thuy Trang T. Nguyen(2), Catherine C. H. Hood(3), and Brian C. Monsell(4)


The U.S. Census Bureau has enhanced the X-12-ARIMA seasonal adjustment program by incorporating an improved automatic regARIMA model (regression model with ARIMA errors) selection procedure. Currently this procedure is available only in test version 0.3 of X-12-ARIMA, but it will be released in a future version of the program. It is based on the automatic model selection procedure of TRAMO, an ARIMA-modeling software package developed by Víctor Gómez and Agustín Maravall (Gómez and Maravall 1997). The procedure of X-12-ARIMA differs from that of TRAMO in several ways, related mainly to parameter and likelihood calculation and to outlier identification. We looked at ways to determine presence of trading day (TD), Easter, and outlier effects to possibly improve the ARIMA model chosen by X-12-ARIMA. We compared models using diagnostics such as out-of-sample forecast error graphs, spectral analysis, Ljung-Box Q statistics, and under certain circumstances, the Hannan-Quinn statistic.

We concluded that we need further research to determine the best procedure for selecting TD and Easter regressors. We have changed the automatic modeling procedure. The F-adjusted Akaike's Information Criterion (AICC) is now the primary selection tool, but the program also uses the regression t-values to eliminate nonsignificant regressors. We could not determine whether changing the outlier critical value during the automatic model selection can improve the final model.


seasonal adjustment; regression model with ARIMA errors; out-of-sample forecast error comparisons; F-adjusted Akaike's Information Criterion

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

(2) Thuy Trang Ta Nguyen is Mathematical Statistican, Decennial Statistical Methods Division, U. S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email :

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

(4) Brian C. Monsell is Mathematical Statistical, 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