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X-11 Symmetric Linear Filters and their Transfer Functions

William Bell and Brian Monsell

RR 92/15


The X-11 seasonal adjustment program can be viewed as being based on linear filters composed of seasonal, nonseasonal, and Henderson trend moving averages. This view is exact for the additive decomposition (apart from modifications to deal with extreme values), and approximate for the multiplicative decomposition (Young 1968). Adopting this view, we consider all the X-11 symmetric linear filters for estimating the seasonal, nonseasonal (seasonally adjusted), trend, and irregular components, that are available from all the possible choices of X-11 filter options (seasonal and Henderson trend moving averages). This report presents graphs of the filter weights and filter squared gains for all these symmetric linear filters.
Source: U.S. Census Bureau | Statistical Research Division | (301) 763-3215 (or |   Last Revised: October 08, 2010