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X-13ARIMA-SEATS Seasonal Adjustment Program

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Sliding Spans Diagnostics for Seasonal and Related Adjustments(1)

David F. Findley(2), Brian C. Monsell(3), Holly B. Shulman(4), and Marian G. Pugh(5)


When are the results of a seasonal adjustment procedure, or other smoothing procedure, likely to be of little value? The diagnostic approach we present offers an answer to this question and to other questions concerned with the comparison of competing adjustments. It is based on a straightforward idea. A minimal requirement of the output of any smoothing or adjustment procedure is Stability: appending or deleting a small number of series values should not substantially change the smoothed values- otherwise, what reliable interpretation can they have? An important related principle is that, for a given series, if only one of several plausible signal extraction procedures has a stable output, then this procedure should be the preferred one for the series. To implement these principles successfully, the definition of stability must be made precise in an appropriate way. Our implementation is focused on multiohcative adjustments produced by the widely-used X-11 seasonal adjustment procedure, but it will be clear that the basic ideas are applicable more widely. The discussion addresses decisions about direct and indirect seasonal adjustment, trading day adjustment, trends, forecast extension prior to adjustment and other common adjustment issues.


Adjustment feability, Indirect adjustments, Trading day adjustments, X-11 and X-ll-ARIMA.

(1) Preprint version of article in Journal of the American Statistical Association, vol. 85 (1990), No. 410, pp. 345-355

(2) 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 :

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

(4) Holly B. Shulman is currently Supervisory Mathematical Statistician, Centers for Disease Control. email :

(5) Marian G. Ewell (Pugh), 1193 Meadow Lane, McLean, VA 22102.

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