Comparing Mean Squared Errors of X-12-ARIMA and Canonical ARIMA Model-Based Seasonal Adjustments

Authored by: William R. Bell , Yea-Jane Chu , George C. Tiao

Economic Time Series

Print publication date:  March  2012
Online publication date:  March  2012

Print ISBN: 9781439846575
eBook ISBN: 9781439846582
Adobe ISBN:


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The fixed filtering approach to seasonal adjustment, as implemented in the original Census X-11 program (Shiskin et al. 1967) and its successors, X-11-ARIMA (Dagum 1975) and X-12-ARIMA (Findley et al. 1998; U.S. Census Bureau 2009), has been widely used by government and industry. This approach relies on a finite set of empirically developed moving averages (MAs). The user can either specify the particular MAs used for a time series or let the program choose them automatically according to some empirical criteria. By contrast, a model-based approach to seasonal adjustment specifies stochastic models for the observed series and underlying components, and derives seasonal adjustment filters from optimal signal extraction theory. The filters used are thus determined by the model form specified, by assumptions made about the component decomposition, and by estimates of the model parameters. (See Bell and Hillmer (1984) for discussion.) The fixed filtering approach is often seen as easier to use, particularly for people with limited statistical backgrounds. The model-based approach, by contrast, offers more flexibility in determining filters and determines its filters according to standard statistical principles.

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