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X-13ARIMA-SEATS Seasonal Adjustment Program

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Seasonal heteroskedasticity in Census Bureau construction series

Thomas M. Trimbur(1)


Seasonal heteroskedasticity exists in a number of monthly time series from major statistical agencies. Accounting for such variation in calendar month effects can be important in estimating seasonal and trend movements. In the context of seasonal adjustment, the standard procedure uses nonparametric (X-11) filters of different lengths in the signal extraction routine of X-12-ARIMA. This serves as a simple, pragmatic procedure that is, however, limited in its ability to adapt to different datasets. In this paper I extend the model-based methodology introduced recently by Proietti (2004) and Bell (2004). I discuss different forms of the seasonal specific model, showing examples of estimation and analysis of trend and seasonal components. A statistical test for seasonal heteroskedasticity is presented and applied to a number of Census Bureau series on housing starts and building permits. It is shown how seasonal noise can be separated from nonsystematic noise and included in the seasonal adjustment of a time series.


seasonal heteroskedasticity, time series, trends, unobserved components.

(1) Thomas M. Trimbur is currently at the U. S. Federal Reserve Board 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