Seasonal Adjustment Methodology at BLS
from: BLS Handbook of Methods, Appendix A.
An economic time series may be affected by regular intrayearly
(seasonal) movements which result from climatic conditions, model
changeovers, vacation practices, and similar factors. Often such effects
are large enough to mask the short-term, underlying movements of the
series. If the effect of such intrayearly repetitive movements can be
isolated and removed, the evaluation of a series may be made more
Seasonal movements are found in almost all economic time series. They
may be regular, yet they do show variation from year to year and are
subject to changes in pattern over time. These changes are most commonly
thought to evolve primarily in a stochastic rather than a deterministic
way. Seasonal adjustment practitioners have long recognized, however, that
some of the year-to-year variation in seasonal movements can be associated
with calendar-related factors such as the number of business or "trading"
days in a month (for series whose monthly estimates are accumulations
across the days of a month) or, of greater concern for some BLS series,
the timing of moving holidays. Recently, variations in the length of
intervals between monthly survey reference periods have also been found to
significantly affect seasonal patterns in some BLS series.
Because the intrayearly seasonal patterns are combined with the
underlying growth or decline and cyclical movements of the series
(trend-cycle) and also random irregularities, it is difficult to estimate
the pattern with exactness. The earliest known attempts to isolate
seasonal factors from time series occurred in the first half of the 20th
century. Some of the early methods depended upon smoothing curves by using
personal judgment. Other formal approaches were periodogram analysis,
regression analysis, and correlation analysis. Because these methods
involved a large amount of work, relatively little application of seasonal
factor adjustment procedures was carried out.
In the mid-1950's, new electronic equipment made more elaborate
approaches feasible in seasonal factor methods as well as in other areas.
The Bureau of the Census developed computer-based seasonal factors based
on a ratio-to-moving-average approach. This was a major step forward, as
it made possible the uniform application of a method to a large number of
series at a relatively low cost. 1 Subsequent improvements in methods and in computer
technology have led to more refined procedures which are both faster and
cheaper than the original techniques.
The Bureau of Labor Statistics began work on seasonal factor methods in
1959. Prior to that time, when additional data became available and
seasonal factors were generated from the lengthened series, the new
factors sometimes differed markedly from the corresponding figures based
on the shorter series. This difference could affect any portion of the
series. It was difficult to accept a process by which the addition of
recent information could affect significantly the seasonal factors for
periods as much as 15 years earlier, especially since this meant that
factors could never become final. The first BLS method, introduced in
1960, had two goals: first, to stabilize the seasonal factors for the
earlier part of the series; second, to minimize the revisions in the
factors for the recent period. Since 1960, the Bureau has made numerous
changes and improvements in its technique and in methods of applying them.
Thus far, all the changes relating to the seasonal adjustment of monthly
series have been made within the scope of ratio-to-moving-average types of
approaches or difference-from-moving-averages types of approaches. The BLS
1960 method, entitled "The BLS Seasonal Factor Method", was further
refined, with the final version being introduced in 1966. It was in
continuous use for many Bureau series (especially employment series based
on the establishment data) until 1980.
In 1967, the Bureau of the Census introduced "The X-11 Variant of the
Census Method II Seasonal Adjustment Program" better known as simply X-11.
The X-11 provided some useful analytical measures along with many more
options than the BLS method. Taking advantage of the X-11's additional
flexibility, BLS began making increasing use of the X-11 method in the
early 1970s, especially for seasonal adjustment of the labor force data
based on the household survey. Later in the 1970s, Statistics Canada, the
Canadian national statistical agency, developed an extension of the X-11
called "The X-11 ARIMA Seasonal Adjustment Method". The X-11 ARIMA
(Auto-Regressive Integrated Moving Average) provided the option of using
modeling and forecasting techniques to extrapolate some extra data at the
end of a time series to be seasonally adjusted. The extrapolated data help
to alleviate the effects of the inherent limitations of the moving average
techniques at the ends of series. After extensive testing and research
showed that use of X-11 ARIMA would help to further minimize revisions in
factors for recent periods, BLS began using the X-11 ARIMA procedure in
1980 for most of its official seasonal adjustment.
None of the aforementioned procedures had any built-in capabilities to
handle the kind of moving-holiday effects found in BLS series, or to
estimate other special effects such as level shifts or survey-interval
effects. In 1989, BLS developed an extension of X-11 ARIMA to allow it to
adjust more adequately for the effects of the presence or absence of
religious holidays in the April survey reference period and of Labor Day
in the September reference period. This extension has been applied since
1989 to a few persons-at-work series, and from 1990 to 1996, was also used
for the adjustment of many of the establishment-survey series on average
weekly hours and manufacturing overtime. In 1989, BLS also introduced
intervention analysis seasonal adjustment (IASA) for selected price index
series. Nonseasonal economic phenomena such as level shifts, seasonal
shifts and outliers can have undesirable effects on the computation of
seasonal factors, and IASA is a technique which allows such phenomena to
be estimated and factored out of series before seasonal factors are
computed. The IASA procedures were also used to compute prior adjustment
factors for the seasonal adjustment of the labor force series beginning in
1994, to control for level shifts associated with the revision introduced
in the Current Population Survey in 1994.
In the meantime, over the several years preceding 1996, the Bureau of
the Census had been working on a significant new extension of X-11. The
new procedure, called X-12 ARIMA, integrates ARIMA forecasting with X-11
seasonal adjustment very much like X-11 ARIMA did, but it also provides a
lot of additional tools including some that enable the estimation and
diagnosis of a wide range of special effects. BLS began using X-12 ARIMA
for the seasonal adjustment of the establishment-survey series effective
with the release of the 1995 benchmark revisions in June 1996, primarily
because of the capabilities it offered for controlling for survey-interval
effects as well as moving holidays.
The standard practice at BLS for current seasonal adjustment of data,
as it is initially released, is to use projected seasonal factors which
are published ahead of time. The time series are generally run through the
seasonal adjustment program once a year to provide the projected factors
for the ensuing months and the revised seasonally adjusted data for the
recent history of the series, usually the last 5 years. It has generally
been unnecessary to revise any further back in time because the programs
which have been used have all accomplished the objective of stabilizing
the factors for the earlier part of the series, and any further revisions
would produce only trivial changes. For the projected factors, the factors
for the last complete year of actual data were selected when the X-11 or
BLS method programs were used.
With the X-11 ARIMA and X-12 ARIMA procedures, the projected year-ahead
factors produced by the program are normally used for labor force and
employment series while the factors for the last complete year are still
used for the price series. For the labor force data since 1980, only the
factors for the January-June period are projected from the annual run—a
special midyear run of the program is done, with up-to-date data included,
to project the factors for the July- December period.
Since 1989, projected factors are also calculated twice a year for use
in seasonally adjusted establishment-based employment, hours, and earnings
data. Factors are projected for the May through October period and
introduced concurrent with the annual benchmark adjustments, and again for
the November-April period. As of the 1996 benchmark adjustments, factors
for the 2 months preceding these respective 6-month periods began to be
revised so that they would be on the same basis as the 6 months of
An alternative to the use of projected factors is concurrent
adjustment, where all data are run through the seasonal adjustment program
each month, and the current observation participates in the calculation of
the current factor. Research has shown potentially significant technical
advantages in the area of minimization of factor revisions that are
possible with concurrent adjustment. Of course, the concurrent approach
precludes the prior publication of factors and requires the expenditure of
substantially more staff and computer time to run, monitor and evaluate
the seasonal adjustment process. If future findings suggest the
desirability of a change to a concurrent procedure or to some other type
of methodology, such a change will be seriously considered in consultation
with the Government's working group on statistics.
In applying any of the above mentioned methods of seasonal adjustment,
the user should be aware that the result of combining series which have
been adjusted separately will usually be a little different from the
direct adjustment of the combined series. For example, the quotient of
seasonally adjusted unemployment divided by seasonally adjusted labor
force will not be quite the same as when the unemployment rate is adjusted
directly. Similarly, the sum of seasonally adjusted unemployment and
seasonally adjusted employment will not quite match the directly adjusted
labor force. Separate adjustment of components and summing of them to the
total usually provides series that are easier to analyze; it is also
generally preferable in cases where the relative weights among components
with greatly different seasonal factors may shift radically. For other
series, however, it may be better to adjust the total directly if high
irregularity among the components makes a good adjustment of all
Finally, it is worth noting that the availability of a fast, efficient
procedure for making seasonal adjustment computations can easily lead to
the processing of large numbers of series without allotting enough time to
review the results. No standard procedure can take the place of careful
review and evaluation by skilled analysts. A review of all results is
strongly recommended. And it should also be remembered that, whenever one
applies seasonal factors and analyzes seasonally adjusted data, seasonal
adjustment is a process which estimates a set of not directly observable
components (seasonal, trend-cycle, irregular) from the observed series and
is, therefore, subject to error. Because of the complex nature of methods
such as X-11 ARIMA, the precise statistical properties of these errors are
1 Shiskin, Julius. Electronic Computers and Business
Indicators, Occasional Paper No. 57, New York, National Bureau of
Economic Research, 1957.
Department of Commerce, Bureau of the Census. Seasonal Analysis of
Economic Time Series, Economic Research Report, ER-1, issued December
Department of Commerce, Bureau of the Census. The X-11 Variant of
the Census Method II Seasonal Adjustment Program. Technical
Paper No. 15 (1967 revision).
Department of Commerce, Bureau of the Census. X-12-ARIMA Reference
Manual, Beta Version 1.1, June 24, 1996.
Department of Labor, Bureau of Labor Statistics. Employment and
Earnings, March and June 1996.
Department of Labor, Bureau of Labor Statistics. The BLS Seasonal
Factor Method, 1966.
Organization for Economic Cooperation and Development. Seasonal
Adjustment on Electronic Computers, Paris, 1961. The report and
proceedings of an international conference held in November 1960.
Describes experience in the United States, Canada, and several European
countries. Includes theoretical sections relating to calendar (trading
day) variation and general properties of moving averages.
Proceedings of a 1976 conference jointly sponsored by the National
Bureau of Economic Research and the Bureau of the Census.
Barton, H.C., Jr., "Adjustment for Seasonal Variation", Federal
Reserve Bulletin, June 1941. The classic account of the FRB
ratio-to-moving-average method, in which the analyst uses skilled judgment
to draw freehand curves at key stages of the procedure.
Buszuwski, James A., and Scott, Stewart., "On the Use of Intervention
Analysis in Seasonal Adjustment," Proceedings of the Business and
Economic Statistics Section, American Statistical Association,
Dagum, Estela Bee. The X-11 ARIMA Seasonal Adjustment Method.
Ottawa, Statistics Canada, January 1983 (Statistics Canada Catalogue
Macaulay, Frederick R. The Smoothing of Time Series, NBER
No. 19. New York, National Bureau of Economic Research, 1931. An
early discussion of moving averages and of the criteria for choosing one
average rather than another.
McIntire, Robert J., "A Procedure to Control for Moving-Holiday
Effects in Seasonally Adjusting Employment and Hours Series",
Proceedings of the Business and Economic Statistics Section,
American Statistical Association, 1990.
Shiskin, Julius. Electronic Computers and Business
Indicators, Occasional Paper No. 57, New York, National Bureau of
Economic Research, 1957. Also published in Journal of Business,
Vol. 30, October 1957. Describes applications of the
first widely used computer program for making seasonal adjustments.
Last Modified Date: February 18, 2014