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X-13ARIMA-SEATS Seasonal Adjustment Program

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Some Recent Developments and Directions in Seasonal Adjustment

David F. Findley(1)


This article provides an overview of some recent areas of development in seasonal adjustment. The emphasis is on areas connected to current and planned versions of SEATS and X-12-ARIMA for the combination program being developed at the U.S. Census Bureau with the support of the Bank of Spain (see Monsell, Aston, and Koopman 2003). This program, tentatively named X-13A-S, offers the user the seasonal adjustment methods of both programs with improved and expanded diagnostics for the model-based seasonal adjustments. For this program, Sections 2–4 cover enhancements to regARIMA modeling capabilities, X-12-ARIMA diagnostics for SEATS adjustments, and improved and new diagnostics for SEATS made available by the signal extraction matrix formulas of Bell and Hillmer (1988) and McElroy and Sutcliffe (2005). Section 5 summarizes the features of four new classes of models for seasonal adjustment or trend estimation presented in Bell (2004), Aston, Findley, Wills, and Martin (2004), Proietti (2004) and Wildi (2004), which might influence the future evolution of X-13A-S or other software. Section 6 briefly summarizes recent methodological developments directed toward enhancing the X-11 seasonal adjustment methodology. Some important topics, such as recent research on methods for trend estimation, receive little mention or none because of limitations of the author’s experience and expertise.


Time series; X-12-ARIMA; SEATS; TSW; RunX12; trends; moving holiday effects; sliding spans; spectrum; phase delay; RegComponent models; sampling error; seasonal heteroscedasticity; uncertainty measures.

(1) David F. Findley was the Senior Mathematical Statistican for Time Series and is now a consultant, 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: April 02, 2015