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X-13ARIMA-SEATS Seasonal Adjustment Program

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X-11 Symmetric Linear Filters and their Transfer Functions

William Bell (1) and Brian C. Monsell (2)


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.

(1) William R. Bell is Senior Mathematical Statistician for Small Area Estimation, U.S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email : william.r.bell@census.gov

(2) Brian C. Monsell is Mathematical Statistican, Statistical Research Division, U. S. Census Bureau, U.S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email : brian.c.monsell@census.gov

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Source: U.S. Census Bureau | Center for Statistical Research and Methodology | (301) 763-1649 (or x12@census.gov) |  Last Revised: November 19, 2012