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X-13ARIMA-SEATS Seasonal Adjustment Program

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On the Spectrum Diagnostics Used by X-12-ARIMA to Indicate the Presence of Trading Day Effects after Modeling or Adjustment

Raymond J. Soukup (1) and David F. Findley (2)


Seasonal adjusters need to know when a time series candidate for seasonal adjustment has trading day effects and when its adjustment for trading day effects has failed to adequately remove these effects. The Census Bureau's X-12-ARIMA seasonal adjustment program calculates several spectra in order to facilitate detection of seasonal and trading day effects that require the adjuster's attention. This paper summarizes the results of a study based on real and simulated time series that led to the current choices made for X-12-ARIMA's trading day spectral diagnostics, including the criteria for warning messages. The features and advantages of the spectrum of the model residuals, which is a new addition to X-12-ARIMA output, are described.


Seasonal Adjustment, Trading day, Spectral analysis, Time series

(1) Raymond J. Soukup is currently a statistican at the Naval Research Laboratories.

(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 :

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