X-11 Symmetric Linear Filters and their Transfer Functions
William Bell and Brian Monsell
RR 92/15
ABSTRACT
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.
