Seasonal Adjustment with the X-11 Method

244 Pages·2001·9.14 MB·English

by  Dominique Ladiray

Lecture Notes in Statistics 158
Edited by P. Bickel, P. Diggle, S. Fienberg, K. Krickeberg,
I. Olkin, N. Wermuth, S.'Zeger
Springer Science+Business Media, LLC
Dominique Ladiray
BenoIt Quenneville
Seasonal Adjustment with
the X-11 Method
, Springer
Dominique Ladiray Benoît Quenneville
EUROSTA T, BECH E4/813 Statistics Canada
Bâtiment Jean Monnet 120 Parkdale Avenue
Rue Alcide de Gasperi 3G-RHC-BSMD
Luxemborg, L-2920 Ottawa, Ontario KIA OT6
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Library of Congress Cataloging-in-Publication Data
Ladiray, Dominique.
Seasonal adjustment with the X-II method I Dominique Ladiray, Benoît Quenneville.
p. cm. - (Lecture notes in statistics; 158)
Includes bibliographical references and index.
ISBN 978-0-387-95171-3 ISBN 978-1-4613-0175-2 (eBook)
DOI 10.1007/978-1-4613-0175-2
I.Seasonal variations (Economics}-Statistical methods. 1. Quenneville, Benoît.
II. Title. 11/. Lecture notes in statistics (Springer-Verlag); v. 158.
HB 137 .L33 2001
330'.0 I '5 I 95-dc21 00-053769
Printed on acid-free paper.
©2001 Springer Science+Business Media New York
Originally published by Springer-Verlag New York, Inc. in 2001
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Camera-ready copy provided by the authoTs.
9 8 7 6 5 4 3 2 1
ISBN 978-0-387-95171-3 SPIN 10788799
To Julius Shiskin, Allan Young, and John Musgrave
Preface
The authors, Dominique Ladiray and Benoit Quenneville, provide a unique
and comprehensive r~view of the X-11 Method of seasonal adjustment.
They review the original X-11 Method developed at the US Bureau of
the Census in the mid-1960's, the X-ll core of the X-ll-ARTMA Method
developed at Statistics Canada in the 1970's, and the X-11 module in the X-
12-ARTMA Method developed more recently at the Bureau of the Census.
The review will prove extremely useful to anyone working in the field of
seasonal adjustment who wants to understand the X-11 Method and how
it fits into the broader picture of seasonal adjustment.
What the authors designate as the X-11 Method was originally desig
nated the X-11 Variant of the Census Method IT Seasonal Adjustment
Program. It was the culmination of the pioneering work undertaken at the
Bureau of the Census by Julius Shiskin in the 1950's. Shiskin introduced the
Census Method T Seasonal Adjustment Program in 1954 and soon followed
it with the introduction of Method TT in 1957.
Tn Method T, seasonal factors were estimated by taking a moving average
of the seasonal-irregular ratios for each month. The seasonal-irregular ra
tios were ratios of the original series to a centered 12-month moving average
that was assumed to represent the trend-cycle component. An alternative
seasonal adjustment was also calculated by substituting a five-month mov
ing average of the first seasonally adjusted series for the centered 12-month
moving average. The most important improvements in Method TT were the
following.
viii Preface
1. The moving averages were extended to the ends of the series by means
of asymmetrical sets of end weights;
2. The five-month moving average used in the second round of Method T
was replaced with a weighted 15-month moving average that provided
a more flexible and smooth curve for the trend-cycle component. Tn
Method T the seasonal factors in the second round were considered al
ternatives that might prove useful for some series. Tn Method TT, there
was no question; the second round seasonal factors were considered
superior;
3. Extreme values in the seasonal-irregular ratios for each month were
identified and modified before seasonal factors were calculated.
Method TI was one of the first uses of the electronic computer for large
scale processing of economic data. The program was run on the two recently
installed Univac computers at the Bureau of the Census. Processing time
for a series of 8 to 10 years of monthly data was about seven minutes.
Tn designing Method TT, Shiskin was familiar with the graphical method
of seasonal adjustment developed before World \Var TT at the Federal Re
serve Board of Governors. This method started with a 12-term moving av
erage of the original data, modified where necessary to better represent the
trend-cycle component. Then, to estimate the seasonal factors, free-hand
curves were drawn through the seasonal-irregular ratios for each month. Tn
drawing these curves the analyst would discount the effect of values consid
ered to be extreme based on knowledge of the industry or process, coupled
with the appearance of the data. Method IT may be viewed as an effort to
instruct a computer to duplicate the procedure that previously had been
applied by skilled professionals.
1 once asked a long time employee of the National Tncome Division of
the US Bureau of Economic A nalysis how the division managed each year
to update and revise seasonal adjustment factors for the GNP data before
electronic computers were available. His reply was "we kept the statistical
clerks all night." These "all nighters" carne at the end of a two or three
month period of additional work on weekends and evenings. The annual
revisions of the national accounts by the BEA are still major undertakings
but staff-wide "all nighters" are no longer necessary. Today they are com
puted in seconds on desktop computers that. are rarely used beyond regular
daytime hours.
Part of the explanation for the success of Method TT was that it was
easy to use. It included graphical output of the several components of the
original series that helped users understand the procedure and assess the
results. The procedure was relatively robust and did not require a strong
background in mathematical statistics.
There are two uses for seasonal adjustment. One is to estimate seasonal
variation for such purposes as production planning and inventory control.
Preface lX
The other is to estimate seasonal variation so as to be able to remove it
from the total variation and thereby expose the other types of variation
more clearly, particularly that reflecting the business cycle.
Shiskin was motivated by the need for government policy-makers to be
provided promptly with assessments of current economic conditions and
short-term forecasts. As long as they were largely independent, it made
good sense to separate the seasonal variation from the cyclical variation
for this purpose. Method IT provided a forecast of the seasonal factors for
the year ahead so that the seasonal variation could be separated quickly
from other types of variation in the estimate for the current. month. (Tt
would be some years before concurrent seasonal adjustments would become
practical and would be demonstrated as better than once-a-year forecasts
of upcoming seasonal factors.) Early on, it was apparent that the revisions
in year-ahead seasonal factors provided by Method TT were often uncom
fortably large when an additional year of data was incorporated.
Tj oined Shiskin at the Bureau in 1958 and John Musgrave came in 1959.
We soon began to focus on improving the original Method IT as well as
assisting Shiskin in the development of business cycle indicators. Successive
experimental variants designated X-I through X-II were developed. The
program for testing rocket-propelled planes inspired the "X" designation.
Tn 1947 Chuck Yeager broke the sound barrier in the X-I, the first of
successively numbered experimental planes. Tn the mid-1960's the X-15,
the last of the rocket-propelled planes, was flying at several times the speed
of sound.
Two of the experimental variants TT, X-3 and X-9, each in turn, replaced
the original Method TT as the official version at the Census Bureau and
some other government agencies. They each included new end weights for
the moving averages ll8ed in estimating the seasonal factors and provided
somewhat smaller revisions.
The X-l0 variant was developed in cooperation with Stephen Marris
who spent a year at the Census Bureau on leave from the Organization
for Economic Cooperation and Development. The X-IO included a family
of moving averages from which the most appropriate was selected for each
month. This approach further reduced revisions in many series. It became
the official OECD method. The approach was not included in the default
version of X-II, but was included as an option. A similar approach was
included in the default version for the trend-cycle component.
Two other persons deserve mention as well. Following the introduction
of Method IT by Shiskin, Duane Evans developed a ratio-to-moving av
erage method of seasonal adjustment at the Bureau of Labor Statistics.
One of the innovations in this program may be viewed as the forerunner
of the expanded treatment of extreme values introduced in the X-II vari
ant. Tn addition, shortly after the introduction of Method TT, the Census
Bureau undertook the development of a parametric approach to seasonal
adjustment under the direction of Harry M. Rosenblatt. Neither of these
x Preface
approaches proved a successful competitor to the X-ll variant, partly be
cause revisions of seasonal factors tended to be larger.
Tn 1965, we certainly did not expect that the X-ll variant of Method TT
would still be playing an important role in seasonal adjustment 35 years
later. It also seemed likely that an approach to measuring the standard
errors in the seasonal factors in X-ll would be developed. The authors are
to be congratulated for an up-to-date review of the X-ll Method. Perhaps
this review will not only help further extend the life of X-ll, but will help
in the development and widespread use of new methods that bear little
resemblance to those of the past.
Allan H. Young Heathsville, Virginia
April 2000
Contents
Preface vii
Introduction 1
1 Brief History of Seasonal Adjustment 5
2 Outline of the X-ll Method 13
2.1 Components and Decomposition Models 13
2.2 Moving Averages . . . . . . . . . . . . . 14
2.3 A Simple Seasonal Adjustment Algorithm 15
2.4 The Basic Algorithm of the X-11 Method 16
2.5 Extreme Observations and Calendar Effects 19
2.6 The Tterative Principle of X-11 ....... 19
2.6.1 Part A: Pre-Adjustments ...... 20
2.6.2 Part B: First Automatic Correction of the Series 20
2.6.3 Part C: Second Automatic Correction of the Series 20
2.6.4 Part D: Seasonal Adjustment . . . . . . . . . . 20
2.6.5 Parts E, F and G: Statistics and Charts . . . . 2]
2.7 From Census X-11 to X-11-ARTMA and X-12-ARTMA 22
3 Moving Averages 23
3.1 Some Definitions and a Little Theory. 23
3.1.1 Definitions and Example. . . . 25
3.1.2 Gain and Phase Shift Functions. 26