Current Population Survey (CPS) 

Technical Documentation 

January 2018 

 

Documentation for prior years is available at 

www.bls.gov/cps/documentation.htm#saarchive 

—————————————— 

Richard B. Tiller and Thomas D. Evans are mathematical statisticians on the Statistical Methods Staff, Office of 

Employment and Unemployment Statistics, Bureau of Labor Statistics. E-mail: Tiller.Richard@bls.gov; 

Evans.Thomas@bls.gov. 

Methodology for Seasonally Adjusting 

National Household Survey Labor Force Series 

with Revisions for 2018

Richard B. Tiller and Thomas D. Evans 

hort-run movements in labor force time series are strongly influenced by seasonality—

periodic fluctuations associated with recurring calendar-related events such as weather, 

holidays, and the opening and closing of schools. Seasonal adjustment eliminates the 

influence of these fluctuations and makes it easier for users to observe fundamental changes in the 

level of the series, particularly changes associated with general economic expansions and 

contractions. 

 While seasonal adjustment is feasible only if the seasonal effects are reasonably stable with 

respect to timing, direction, and magnitude, these effects are not necessarily fixed, and often evolve 

over time. The evolving patterns are estimated by X-13ARIMA-SEATS (X-13), with procedures 

based on moving averages, or “filters,” that successively average a shifting timespan of data, 

thereby providing estimates of seasonal factors that change in a smooth fashion from year to year. 

 For observations in the middle of a series, a set of symmetric moving averages with fixed 

weights produces final seasonally adjusted estimates. A filter is symmetric if it is centered around 

the time point being adjusted, with an equal amount of data preceding and following that point. 

Standard seasonal adjustment options imply a symmetric filter that uses from 6 to 10 years of 

original data to produce a final seasonally adjusted estimate. Obviously, this final adjustment can be 

made only where there are enough data beyond the time point in question to adjust with the 

symmetric filter. 

 To seasonally adjust recent data, shorter filters with less desirable properties must be used. 

These filters are referred to as asymmetric, because they use fewer observations after the reference 

point than preceding it. The weights for such filters vary with the number of observations that are 

available beyond the time point for which estimates are to be adjusted. Seasonally adjusted data for 

the current year are produced with a technique known as concurrent adjustment. Under this 

practice, the current month’s seasonally adjusted estimate is computed with the use of all relevant 

original data up to and including data for the current month. Revisions to estimates for previous 

months, however, are postponed until the end of the year. Revisions to a seasonally adjusted 

estimate for a given time point continue until enough future observations become available to use 

the symmetric weights. This effectively means waiting up to 5 years for a final adjustment when 

standard options are used. 

S
2

 At the end of each calendar year, BLS reestimates the seasonal factors for the Current 

Population Survey (CPS, or Household Survey) series by including another full year of data in the 

estimation process. On the basis of this annual reestimation, BLS revises the historical seasonally 

adjusted data for the previous 5 years. As a result, each year’s data are generally subject to five 

revisions before the values are considered final. The fifth and final revisions to data for the earliest 

of the 5 years are usually quite small, while the first-time revisions to data for the most recent years 

are generally much larger. For the major aggregate labor force series, however, the first-time 

revisions rarely alter the essential trends observed in the initial estimates. 

Changes in 2018 

Revisions to 2017 estimates 

This year’s revisions incorporate data through December 2017 and provide revised estimates for 

January 2013 through November 2017 for all previous seasonally adjusted labor force series. 

Currently, there are 153 series that are directly seasonally adjusted and many more that are derived 

from these series. (See the subsequent section titled “Aggregation procedures.”) 

 Effective with the release of December 2017 labor force data, the X-13 time series models in the 

seasonal adjustment process use 2003 as the beginning year for all directly-adjusted series. As a 

result, some of the X-13 settings changed for many series. These changes tend to make little 

difference in the final seasonally adjusted labor force series. For more information about the 

selection of X-13 input series lengths, see the subsequent section, “Time Series Modeling, Model 

adequacy and length of series.” 

 An important criterion for evaluating alternative methods of seasonal adjustment is how close 

initial estimates are to the results of subsequent revisions. Users of seasonally adjusted data are 

often most interested in current information. Thus, it is desirable that the initial seasonally adjusted 

estimates be as close as possible to the improved estimates made after more data become available. 

Even though the revisions currently being released for the 2017 seasonally adjusted data are not 

final, the first revisions are usually the largest and often indicate the direction of subsequent 

revisions. 

 Table 1 shows the civilian unemployment rates for January to November 2017, as first 

computed and as revised, and there was one small revision. Note that December 2017 is the final 

month of the series and has no revision. 
3

Table 1. Seasonally adjusted unemployment rates in 2017 and change due to revision

January ......................................... 4.8 4.8 0.0

February ..................................................... 4.7 4.7 0

March ...................................................... 4.5 4.5 0

April ............................................. 4.4 4.4 0

May ................................................. 4.3 4.3 0

June ..................................................... 4.4 4.3 -.1

July .............................................. 4.3 4.3 0

August .......................................... 4.4 4.4 0

September ............................................ 4.2 4.2 0

October ........................................ 4.1 4.1 0

November ....................................................................................................... 4.1 4.1 0

Month As first

computed As revised Change

Extension of seasonal adjustment to additional series 

No new seasonally adjusted series were added for 2018.

Adjustment Methods and Procedures 

Beginning in 2003, BLS adopted the use of X-12-ARIMA (X-12) as the official seasonal 

adjustment procedure for CPS labor force series, replacing the X-11-ARIMA (X-11) program that 

had been used since 1980. Both X-12-ARIMA and X-11-ARIMA are based on earlier versions of 

the widely used X-11 method developed at the U.S. Census Bureau in the 1960s.1 Statistics Canada 

added to X-11 the ability to extend the time series with forward and backward extrapolations from 

Auto-Regressive Integrated Moving Average (ARIMA) models, prior to seasonal adjustment. The 

X-11 algorithm for seasonal adjustment is then applied to the extended series. When adjusted data 

are revised after future data become available, the use of forward extension results in initial 

seasonal adjustments that are subject to smaller revisions, on average. 

The enhancements in X-12 fall into three basic categories: (1) Enhanced ARIMA model 

selection and estimation, (2) detection and estimation of outlier, trading day, and holiday effects, 

and (3) new post adjustment diagnostics. 

 

1

 For a detailed discussion of X-12-ARIMA, see David F. Findley, Brian C. Monsell, William R. Bell, Mark C. 

Otto, and Bor-Chung Chen, “New Capabilities and Methods of the X-12-ARIMA Seasonal Adjustment Program,” 

Journal of Business and Economics Statistics, April 1998, pp. 127-152, www.census.gov/ts/papers/jbes98.pdf. For 

documentation on X-11-ARIMA, see Estela Bee Dagum, The X-11 ARIMA Seasonal Adjustment Method, catalogue no. 

12-564E (Ottawa, Statistics Canada, January 1980), available on the U.S. Census Bureau’s website at 

www.census.gov/srd/www/sapaper/historicpapers.html. The X-11 method is described in Julius Shiskin, Alan Young, 

and John Musgrave, “The X-11 Variant of the Census Method II Seasonal Adjustment Program,” Technical Paper no. 

15 (Bureau of the Census, 1967), also available at the link immediately above. 
4

 Starting with 2015, BLS moved to the X-13 program,2 which was developed by the U.S. Census 

Bureau and the Bank of Spain. The X-13 program includes all of the capabilities of the X-12 

program, while adding the SEATS seasonal adjustment methodology. 3

 X-11 and SEATS have strong similarities. The ARIMA model of the observed series is the 

starting point for both. They both also use the same basic estimator, which is a weighted moving 

average of the series to produce the seasonally adjusted output. Their methods differ in the 

derivation of their moving average weights. (See the subsequent section titled “X-11 and SEATS 

decompositions.”) 

 X-11 is empirically based. It directly selects the seasonal moving averages from a pre-specified 

set. The weights are not designed for any specific series, but fit a wide variety of series. SEATS is 

model based and derives a moving average from the ARIMA model of the series. The moving 

averages are tailored to the specific modeled properties of the series. The SEATS methodology is 

flexible in that it can adjust some series that X-11 finds too variable. It also facilitates analysis with 

a variety of error measures produced within the system. 

 For almost all of the national labor force series that are seasonally adjusted by BLS, the main 

steps of the seasonal adjustment process proceed in the following order: 

1) Time series modeling—a REGARIMA model (a combined regression and ARIMA 

model) is developed to account for the normal evolutionary behavior of the time series 

and to control for outliers and other special external effects that may exist in the series; 

2) Prior adjustments—given an adequate REGARIMA model, the series is modified by 

prior adjustments for external effects estimated from the regression part of the model and 

extrapolated forward 24 months or more by the ARIMA part of the model; 

3) X-11 or SEATS decomposition—the modified and extrapolated series is decomposed 

into trend-cycle, seasonal, and irregular components by means of a series of moving 

averages, to produce seasonal factors for implementing seasonal adjustment; and 

4) Evaluation—a battery of diagnostic tests is produced to evaluate the quality of the final 

seasonal adjustment. 

 

Time series modeling

Time series models play an important role in seasonal adjustment. They are used to identify and 

adjust the series for atypical observations and other external effects, as well as to extend the original 

series with backcasts and forecasts so that fewer asymmetric filters can be used at the beginning and 

end of the series. 

 

 

2

 For documentation on X-13ARIMA-SEATS, see The X-13ARIMA-SEATS Reference Manual, (Washington, Bureau of 

the Census, September 2013), www.census.gov/ts/x13as/docX13AS.pdf. 

3

 For documentation on the SEATS program, which was developed by Victor Gomez and Agustin Maravall, see 

“Seasonal Adjustment and Signal Extraction in Economic Time Series,” in D. Peña, G.C. Tiao, and R.S. Tsay (eds.), A 

Course in Time Series Analysis, Ch.8, 202-247, New York: J. Wiley and Sons, 2001, 

www.bde.es/f/webbde/SES/servicio/software/tramo/sasex.pdf. 
5

ARIMA models4are designed to make forecasts of a time series based on only its past values. 

While these models can represent a wide class of evolving time series patterns, they do not account 

for the presence of occasional outliers and other special external effects. An outlier represents a 

sudden break in the normal evolutionary behavior of a time series. Ignoring the existence of outliers 

may lead to serious distortions in the seasonally adjusted series. 

 A common form of outlier that presents a special problem for seasonal adjustment is an abrupt 

shift in the level of the data that may be either transitory or permanent. Three types of outliers are 

usually distinguished: (1) An additive change that affects only a single observation, (2) a temporary 

change having an effect that diminishes to zero over several periods, and (3) a level shift or a break 

in the trend of the data, which represents a permanent increase or decrease in the underlying level of 

the series. These three main types of outliers, as well as other types of external effects, may be 

handled by the time series modeling component of X-13. This is done by adding to the ARIMA 

model appropriately defined regression variables based on intervention analysis originally proposed 

by George E.P. Box and George C. Tiao.5

 The combined regression and ARIMA model is referred to as a REGARIMA model and is 

represented by 

Y X Z t t t    ,

where Yt is the original series or a logarithmic transformation of it; Xt is a set of fixed regression 

variables;  represents the regression coefficients, and Zt is a standard seasonal ARIMA model 

described by the notation (p,d,q)(P,D,Q), where p is the number of regular (nonseasonal) 

autoregressive parameters, d is the number of regular differences, q is the number of regular moving 

average parameters, P is the number of seasonal autoregressive parameters, D is the number of 

seasonal differences, and Q is the number of seasonal moving average parameters. 

 While the ARIMA model can be very complicated theoretically, in practice it takes a 

parsimonious form involving only a few estimated parameters. There are well-developed methods 

for determining the number and types of parameters and the degree of differencing appropriate for a 

given series. 

 With respect to specifying the regression component to control for outliers, X-13 offers two 

approaches. First, major external events, such as breaks in trend, are usually associated with known 

events. In such cases, the user has sufficient prior information to specify special regression variables 

to estimate and control for these effects. 

 Second, because it is rare that there is sufficient prior information to locate and identify all of 

the atypical observations that may exist in a time series, as a second approach to specifying the 

regression component, REGARIMA offers automatic outlier detection based on work by I. Chang, 

G.C. Tiao, and C. Chen.6 This approach is especially useful when a large number of series must be 

 

4

 For a more detailed discussion of ARIMA models, refer to George E.P. Box and Gwilym M. Jenkins, Time Series 

Analysis: Forecasting and Control (San Francisco, Holden Day, 1970); and Sir Maurice Kendall and J. Keith Ord, Time 

Series (New York, University Press, 1990). 

5

 George E.P. Box and George C. Tiao, “Intervention Analysis with Applications to Economic and Environmental 

Problems,” Journal of the American Statistical Association, vol. 70, no. 353, 1975, pp. 71-79.

6

 I. Chang, G.C. Tiao, and C. Chen, “Estimation of Time Series Parameters in the Presence of Outliers,” 

Techonometrics, 1988, pp. 193-204.
6

processed. Of course, both approaches may be combined so that readily available prior information 

can be used directly, while unknown substantial outliers may still be discovered. 

Model adequacy and length of series. The preference is to use relatively long series in fitting time 

series models, but with some qualifications. Sometimes, the relevance of data in the distant past to 

seasonal adjustment is questionable, which may lead to using a shorter series. 

 Even though the filters have limited memory, there are reasons for using longer series. First, for 

homogenous time series, the more data used to identify and estimate a model, the more likely it is 

that the model will represent the structure of the data well and the more accurate the parameter 

estimates will be. The exact amount of data needed for time series modeling depends on the 

properties of the series involved. Arbitrarily truncating the series, however, may lead to more 

frequent changes in model identification and to large changes in estimated parameters, which in turn 

may lead to larger-than-necessary revisions in forecasts. 

 Second, although level shifts and other types of outliers tend to occur more often in longer 

series, X-13 has the capability of automatically controlling for these effects. Third, some very useful 

diagnostics available in X-13 typically require a minimum of 11 years of data and, in some cases, as 

much as 14 years of data. Fourth, attempting to fit longer series often provides useful insights into 

the properties of the series, including their overall quality and the effects of major changes in survey 

design.

Extensive use is made of intervention analysis to estimate the magnitude of known breaks in 

CPS series and of automatic outlier detection to identify and correct for the presence of additional 

atypical observations. Once a model is estimated, it is evaluated in terms of its adequacy for 

seasonal adjustment purposes. The criteria essentially require a model to fit the series well (there 

should be no systematic patterns in the residuals) and to have low average forecasting errors for the 

last 3 years of observed data. When there is a tradeoff between the length of the series and the 

adequacy of the model, a shorter series is selected. In this case, the identification of the model is not 

changed with the addition of new data unless the model fails diagnostic testing. 

 Acceptable REGARIMA models have been developed for all of the labor force series that are 

directly adjusted. (For information about directly and indirectly adjusted series, see the subsequent 

section titled “Aggregation procedures.”) 

Prior adjustments 

Prior adjustments are adjustments made to the original data prior to seasonal adjustment. Their 

purpose is to adjust the original series for atypical observations and other external effects that 

otherwise would seriously distort the estimates of the seasonal factors. Prior adjustment factors are 

subtracted from or used as divisors for the original series, depending on whether the seasonal 

adjustment is additive or multiplicative. 

 Prior adjustment factors may be based on special user-defined adjustments or handled more 

formally with REGARIMA modeling. Currently, all prior adjustment factors for the national 

household survey labor force series are estimated directly from REGARIMA. 

Level shifts. The most common type of outlier that occurs in CPS series is the permanent level shift. 

Most such shifts have been due to noneconomic methodological changes related to revisions in 
7

population controls and to major modifications to the CPS design. One notable economic level shift 

was due to the 2001 terrorist attacks. 

 At present, there are no prior adjustments for major level shifts due to population control 

revisions. (The input series currently used for seasonal adjustment begin with 2003; the last major 

level shift from a population control revision occurred prior to then.) A few labor force series 

include level shifts in the REGARIMA models; these are due to effects from the Great Recession 

(December 2007–June 2009). 

 Population estimates extrapolated from the latest decennial census are used in the second-stage 

estimation procedure to control CPS sample estimates to more accurate levels. These intercensal 

population estimates are regularly revised to reflect the latest information on population change. 

 During the 1990s, three major breaks occurred in the intercensal population estimates. 

Population controls based on the 1990 census, adjusted for the estimated undercount, were 

introduced into the CPS series in 1994 and, in 1996, were extended back to 1990. In January 1997 

and again in January 1999, the population controls were revised to reflect updated information on 

net international migration. 

 Population revisions, which reflected the results of Census 2000, were introduced with the 

release of data for January 2003 and were extended back to data beginning in January 2000. Since 

2003, the population controls have been updated each January to reflect new estimates of net 

international migration in the postcensus period, updated vital statistics and other information, and 

any methodological changes in the population estimation process. The population revisions 

introduced in January 2012 incorporated the results of the 2010 Census; those revisions were not 

extended back to January 2010. Further information on CPS population controls for 1996 to the 

present is available on the BLS website at www.bls.gov/cps/documentation.htm#pop.

 In 1994, major changes to the CPS were introduced, including a redesigned and automated 

questionnaire and revisions to some of the labor force concepts and definitions. In January 2003, 

new industry and occupational classifications also were introduced and were extended back to data 

beginning in 2000. 

 To test for the possibility that revisions to the population controls or significant survey changes 

have important effects on those CPS series with large numerical revisions, each REGARIMA model 

is modified to include intervention variables for those years. The coefficients for these variables 

provide estimates of the direction and magnitude of the intervention effects. 

 Intervention effects for 2000 were necessary for selected employment series related primarily to 

Hispanic, adult, and agricultural categories. These effects mainly reflect increases in adult and 

Hispanic employment due to the introduction of Census 2000-based population controls and a 

decline in agricultural employment caused by the change in the industry classification system.7

 Due to an unusual revision in the population controls in January 2000, the unadjusted 

employment level of Black or African American men 20 years or over had a strong upward shift in 

 

7

 See “Revisions to the Current Population Survey Effective in January 2003” at www.bls.gov/cps/rvcps03.pdf. 
8

the first quarter of 2000. This temporary effect was permanently removed from the seasonally 

adjusted series with the use of the REGARIMA model. 

Effect of September 2001. At the end of 2001, unemployed job losers were identified as having had 

substantial upward level shifts one month after the September 11, 2001, terrorist attacks on the 

World Trade Center in New York City.8 Also, four additional series related to workers employed 

part time for economic reasons were identified as having substantial upward shifts at the time of the 

terrorist attacks. 

Calendar effects. Calendar effects are transitory level shifts in a series that result from calendar 

events such as moving holidays or the differing composition of weekdays in a month between years. 

These effects have different influences on the same month across years, thereby distorting the 

normal seasonal patterns for the given month. 

 Two CPS series related to persons at work previously exhibited significant effects in their April 

data due to the timing of Easter: “persons at work on part-time schedules for noneconomic reasons 

who usually work part time in all industries” and “persons at work on part-time schedules for 

noneconomic reasons who usually work part time in nonagricultural industries.” These series were 

seasonally adjusted with multiplicative models with a moving-holiday correction. A detailed 

discussion of the nature of the Easter effect in those series and of the procedure used to control for it 

was included in the January 1990 version of this article. However, after testing for Easter effects 

with both series beginning in 2003 (the current start year in the time series models), diagnostic 

results indicated that prior adjustments for Easter are no longer needed. 

X-11 and SEATS decompositions 

The X-11 and SEATS methods of seasonal adjustment contained within the X-13 program assume 

that the original series is composed of three components: trend-cycle, seasonal, and irregular. 

Depending on the relationship between the original series and each of the components, the mode of 

seasonal adjustment may be additive or multiplicative. Formal tests are conducted to determine the 

appropriate mode of adjustment. 

 The multiplicative mode assumes that the absolute magnitudes of the components of the series 

are dependent on each other, which implies that the size of the seasonal component increases and 

decreases with the level of the series. With this mode, the monthly seasonal factors are ratios, with 

all positive values centered around unity. The seasonally adjusted series values are computed by 

dividing each month’s original value by the corresponding seasonal factor. 

 In contrast, the additive mode assumes that the absolute magnitudes of the components of the 

series are independent of each other, which implies that the size of the seasonal component is 

independent of the level of the series. In this case, the seasonal factors represent positive or negative 

deviations from the original series and are centered around zero. The seasonally adjusted series 

values are computed by subtracting the corresponding seasonal factor from each month’s original 

value. 

 Most seasonally adjusted CPS series are adjusted using the X-11 component of X-13. X-11 

applies a sequence of moving average and smoothing calculations to estimate the trend-cycle, 

 

8

 For more details, see www.bls.gov/cps/cpsrs2002.pdf. 
9

seasonal, and irregular components. The method takes either a ratio-to- or difference-from-movingaverage approach, depending on whether the multiplicative or additive model is used. For 

observations in the middle of the series, a set of fixed symmetric moving averages (filters) is used to 

produce final estimates. The implied length of the final filter under standard options is 72 time 

points for the 3 by 5 seasonal moving average or 120 time points for the 3 by 9 moving average. 

That is, a final seasonally adjusted estimate for a single time point requires up to 5 years of monthly 

data preceding and following that time point. For recent data, asymmetric filters, with less desirable 

properties than symmetric filters, must be used. 

Some seasonally adjusted CPS series are adjusted using the SEATS component of X-13 rather 

than the X-11 component. Like X-11, SEATS decomposes the observed series into trend, seasonal, 

and irregular components and its relationship between the components may be additive or 

multiplicative (via a log transformation). Both X-11 and SEATS use moving averages to 

decompose the series. The major difference between the two procedures is how the moving 

averages are constructed. X-11 selects from a set of predefined filters while SEATS derives its 

filters from a decomposition of the ARIMA model fit to the observed series into models for the 

trend, seasonal, and irregular components. The SEATS filters therefore are more tailored to the 

specific properties of the series as reflected in the ARIMA model fit while X-11 filters are 

nonparametric in that they can fit a wide variety of series without depending on a specific model. 

Evaluation 

A series should be seasonally adjusted if three conditions are satisfied: the series is seasonal, the 

seasonal effects can be estimated reliably, and no residual seasonality is left in the adjusted series. A 

variety of diagnostic tools is available for X-11 to test for these conditions. Among these tools are 

the F test from the original X-11, the more extensive M and Q tests from X-11-ARIMA, and a set of 

tests first available in X-12. The latter include sliding-span diagnostics, frequency-spectrum 

estimates, and revision-history statistics. X-13 provides some of the above diagnostics for SEATS 

analysis, but also provides a battery of model-based diagnostics. If diagnostic testing shows that any 

of the three conditions listed fails to hold for a given series, that series is deemed not suitable for 

seasonal adjustment. 

Due to the strong effects on labor force series from the Great Recession, there were many 

criticisms and comments from various sources about these effects on CPS seasonally adjusted 

series. Evans and Tiller (2013) addressed possible Great Recession effects on CPS national 

seasonally adjusted series and found no evidence of trend or seasonal breaks that biased the 

adjustments during the postrecession period. The article is available at 

www.bls.gov/osmr/pdf/st130200.pdf. 

Concurrent seasonal adjustment 

Concurrent seasonal adjustment of national labor force data began at BLS with the release of 

estimates for December 2003 in January 2004. This practice replaced the projected-factor method, 

which updated seasonal factors only twice a year. Under the latter procedure, projected seasonal 

factors were used to seasonally adjust the new original data as they were collected. At midyear, the 

historical series were updated with data for January through June, and the seasonal adjustment 

program was rerun to produce projected seasonal factors for July through December of the current 

year. 
10

 With concurrent seasonal adjustment, the seasonal adjustment program is rerun each month as 

the latest CPS data become available. The seasonal factors for the most recent month are produced 

by applying a set of moving averages to the entire data set, extended by extrapolations, including 

data for the current month. While all previous-month seasonally adjusted estimates are recalculated 

in this process, BLS policy is to not revise previous months’ official seasonally adjusted estimates 

as new data become available during the year. Instead, revisions are introduced for the most recent 

5 years of data at the end of each year. 

 Numerous studies, including that discussed in a 1987 paper9on the CPS labor force series, have 

indicated that concurrent adjustment generally produces initial seasonally adjusted estimates 

requiring smaller revisions than do estimates produced with the projected-factor method. Revisions 

to data for previous months also may produce gains in accuracy, especially when the original data 

are themselves regularly revised on a monthly basis. Publishing numerous revisions during the year, 

however, can confuse data users. 

 The case for revisions to previous-month seasonally adjusted estimates is less compelling for 

CPS series, because the original sample data normally are not revised. Moreover, an empirical 

investigation indicated that there were no substantial gains in estimating month-to-month changes 

by introducing revisions to the data for the previous month. For example, it was found that if 

previous-month revisions were made to the labor force series, the overall unemployment rate would 

be different in only 2 months between January 2001 and November 2002, in each case by only onetenth of a percentage point. (More detailed information about this study is available from the 

authors upon request.) 

Aggregation procedures

BLS directly seasonally adjusts series on the basis of age, sex, industry, education, and other 

characteristics. BLS also provides seasonally adjusted totals, subtotals, and ratios of selected series. 

It is possible to seasonally adjust an aggregate series either directly or indirectly by seasonally 

adjusting its components and adding the results, or dividing in the case of ratios. Indirect and direct 

adjustments usually will not give identical results, because (1) seasonal patterns vary across series, 

(2) there are inherent nonlinearities in X-13, (3) many series are multiplicatively adjusted, and (4) 

some series are ratios. 

 BLS uses indirect seasonal adjustment for most of the major labor force aggregates. Besides 

retaining, so far as possible, the essential accounting relationships, the indirect approach is needed 

because many of the aggregates include components with different seasonal and trend 

characteristics that sometimes require different modes of adjustment. 

 Examples of indirectly seasonally adjusted series are the levels of total unemployment, 

employment, and the civilian labor force, as well as the unemployment rate for all civilian workers. 

These series are produced by the aggregation of some or all of the seasonally adjusted series for the 

eight major civilian labor force components. The seasonally adjusted level of total unemployment is 

the sum of the seasonally adjusted levels of unemployment for four age-sex groups: men 16 to 19 

years, women 16 to 19 years, men 20 years and over, and women 20 years and over. Likewise, 

seasonally adjusted civilian employment is the sum of employment in all industries for the same 

 

9

 See George R. Methee and Robert J. McIntire, “An Evaluation of Concurrent Seasonal Adjustment for the Major 

Labor Force Series,” in Proceedings of the Business and Economic Statistics Section (Alexandria, VA, American 

Statistical Association, 1987), available at www.bls.gov/cps/methee_mcintire_asa_1987.pdf. 
11

four age-sex groups. The seasonally adjusted civilian labor force is the sum of all eight components. 

The seasonally adjusted civilian unemployment rate is computed as the ratio of the total seasonally 

adjusted unemployment level to the total seasonally adjusted civilian labor force (expressed as a 

percentage). 

 A problem with producing seasonally adjusted estimates for a series by aggregation is that 

seasonal adjustment factors cannot be directly computed for that series. Implicit seasonal 

adjustment factors, however, can be calculated after the fact by taking the ratio of the unadjusted 

aggregate to the seasonally adjusted aggregate or, for additive implicit factors, the difference 

between those two aggregates. 

Availability of revised series 

These revisions replace the seasonally adjusted estimates previously published. Revised historical 

seasonally adjusted labor force data are available in various forms on the BLS website at

www.bls.gov/cps/data.htm, including text file access at https://download.bls.gov/pub/time.series/ln/

to all of the revised data. The seasonally adjusted data last published for 2012 and earlier years were 

not further revised.