Comparing seasonal adjustment
and trend extraction lters with
application to a model-based
selection of X11 linear lters
Keywords: Signal Extraction, Unobserved Components Arima, Seasonal Adjust-
ment, Trends, X12, Distance Measure.
eurostat, Luxembourg, email: email@example.com
Joint Research Centre, Ispra, email: firstname.lastname@example.org. Correspondance should be ad-
dressed to C.Planas, Joint Research Centre, TP361, Via E.Fermi, 1, I-21020 Ispra (VA), Italy.
This paper was written within the framework of a study on Seasonal Adjustment methods, con-
ducted for Eurostat (contract nr. 6663002 to the second author). The ideas expressed here are the
authors' and do not necessarily re
ect the position of Eurostat. Thanks are due to the Members
of Eurostat's internal task-force on Seasonal Adjustment for their remarks and suggestions.
In this paper, data-ltering methods for decomposing univariate time series into orthogonal
components such that seasonal, trend and noise, are compared. The attention focuses on
two important cases often met in applied time series analysis, trend extraction and seasonal
adjustment. Emphasis is put on situations where large set of time series are decomposed,
so the comparison procedure that we build is primarily designed for large-scale problems.
Empirical methods like X11 and and a model-based method like Arima signal extraction
are considered. The aim of this paper is to develop simple tools able to inform practitioners
about: (i) how close the empirical and model-based procedures outputs may be expected
to be; (ii) how to select the X11 empirical lters in order to reduce as much as possible
the discrepancies; (iii) the type of discrepancies expected between model-based lters and
the corresponding closest X11 lter. The discussion is general enough so as to concern all
the historical lters embodied in X11 and its variants.
In this paper, data-ltering methods for decomposing univariate time se