42  Monthly Labor Review • October 2012

CES Seasonal Adjustment

Jurgen Kropf

and

Nicole Hudson The Current Employment Statistics 

(CES) survey, conducted monthly by 

the Bureau of Labor Statistics (BLS), 

obtains data on payroll employment, hours, 

and earnings from business establishments 

and produces industry-based estimates. The 

month-to-month movements in these estimates are timely indicators of the overall 

strength and direction of the nation’s economy and, as such, are closely followed by policymakers and forecasters. Over-the-month 

changes in CES series are nearly always analyzed on a seasonally adjusted basis; therefore, accurate seasonal adjustment is an important component in the usefulness of these 

monthly data. Standard seasonal adjustment 

methodology relies heavily on the most recent 3 years to determine the expected seasonal change in employment for each month 

of the current year.

Seasonal adjustment and the recession

Recently, a concern has arisen as to whether 

the 2007–2009 recession has created a bias 

in the factors that are used in seasonal adjustment. The concern is that those factors 

may be causing a pattern of stronger increasJurgen Kropf is

Division Chief,

Division of Industry

Data Development,

Office of Employment

and Unemployment 

Statistics. Nicole

Hudson is an economist

in the same division.

Email: kropf.jurgen@bls.

gov or hudson.nicole@

bls.gov.

Current Employment Statistics seasonal 

adjustment and the 2007–2009 recession

Removing the declines due to the 2007–2009 recession

prior to seasonal adjustment in a number of experimental

data series reveals that the recession did not create

any bias causing a pattern of stronger increases in employment

in the winter months of the fourth through the first quarter

versus weaker increases from the second to the third quarter

es running from the fall and winter months 

making up the fourth quarter of one year 

through the first quarter of the next, compared with weaker increases occurring in 

the spring and summer months composing 

the second quarter of the year through the 

third quarter of the same year, in the most 

recent years after the recession. (See chart 

1.) Specifically, the extreme declines seen in 

the recession in the fourth quarter of 2008 

and first quarter of 2009 may have been 

absorbed into the seasonal factor currently 

used to calculate seasonally adjusted data 

for recent months. To address this issue, the 

analysis that follows applies an experimental treatment using additional outliers prior 

to seasonal adjustment in order to remove 

the effect of the recession. Although existing CES program standard practice permits 

the treatment of point outliers (i.e., outliers 

affecting only 1 month), the experimental treatment allows for additional outliers, 

including level shifts and ramps (affecting 

consecutive months). The analysis compares 

the experimental treatment with the original 

treatment to determine whether removing 

the effects of the recession affects the distribution of the seasonally adjusted employ-
Monthly Labor Review • October 2012  43

ment increases across quarters.

Existing seasonal adjustment procedure

The CES program uses X-12-ARIMA software for seasonal adjustment. Developed by the Census Bureau, 

X-12-ARIMA uses a common time series decomposition 

method (see Appendix A) and a weighted moving average to estimate the components of seasonal adjustment.1

 The CES program employs a concurrent seasonal 

adjustment methodology in which new seasonal factors 

are calculated each month, incorporating all relevant data 

up to and including data for the current month.2 Prior 

to seasonal adjustment, the estimates (input data) are 

adjusted to remove known nonseasonal events, such as 

strikes, to ensure that these events are not included in 

the calculation of the seasonal factors. In addition, the X12-ARIMA automatic outlier detection procedure is used 

to identify and adjust for point outliers, also called additive outliers, which affect only 1 month. This is done 

to prevent extreme values from distorting the seasonal 

factors. Once the seasonal factors are calculated, they are 

applied to the original, non-seasonally-adjusted data to 

calculate the seasonally adjusted estimate. Multiplicative 

or additive seasonal adjustment is used, depending on the 

seasonal variation of the series. Seasonal adjustment is 

performed at the three-digit North American Industry 

Classification System level, and more detailed levels for 

some industries. Both direct and indirect seasonal adjustment methods are used to generate the CES seasonally 

adjusted employment series. The total nonfarm seasonally 

adjusted employment series is generated indirectly by aggregating 158 directly adjusted series.3

Removing the impact of the recession

The aforesaid experimental outlier treatment is used to 

evaluate concerns that the existing procedure does not 

sufficiently account for all recession-related effects.4 The 

experimental treatment uses additional types of outliers 

that are not used in the existing procedure for removing 

the effect of the recession from the non-seasonally-adjustChart 1. Month-to-month change in total nonfarm seasonally adjusted employment, January 2008–June 2012

2008 2009 2010 2011 2012

600

400

200

0

–200

–400

–600

–800

–1,000

Fourth quarter, 2008,

to first quarter, 2009

Fourth quarter, 2009,

to first quarter, 2010

Fourth quarter, 2010,

to first quarter, 2011

Fourth quarter, 2011,

to first quarter, 2012

SOURCE: U.S. Bureau of Labor Statistic

Thousands Thousands

600

400

200

0

–200

–400

–600

–800

–1,000
CES Seasonal Adjustment

44  Monthly Labor Review • October 2012

ed data prior to seasonal adjustment. The additional types of 

outlier are (1) level shifts, in which there is a sudden change 

in the level of the series in a particular month and the series 

continues at a new level in the months that follow, (2) temporary changes, in which there is a sudden change in the level 

of the series in a particular month and the series slowly returns to the previous level in the months that follow, and (3) 

ramps, in which there is a gradual change in the level of the 

series and the series continues at the new level. (See Appendix B.) Additive outliers, temporary changes, and level shifts 

can be automatically detected by the X-12-ARIMA software; 

ramps, however, must be defined manually.

Many industries experienced a gradual change due to the 

recession, rather than a sudden change in the level of the series. Typically, the change lasted 6 months or more, but it varied with the industry. To remove the impact of the 2007–2009 

recession prior to seasonal adjustment, ramps were fitted to 

each series that displayed a significant decline during the recession. In order to use ramps, the X-12-ARIMA software requires that a beginning and ending date be specified for the 

ramp of each series. Because the timespan of the decline 

due to the recession varied across industries, the beginning and ending date of the ramp for each industry varies 

as well. To determine these dates, the peak and trough in 

each industry were identified with methods developed by 

researchers at the National Bureau of Economic Research 

(NBER).5 The dates of the peaks and troughs were used to 

define the dates of the ramps for the X-12-ARIMA software for most industries. The beginning and ending dates 

of the ramps do not necessarily correspond to the official 

peaks and troughs. In addition to the manually identified 

ramps, the automatically identified types of outlier were 

used to adjust the original series for extreme values prior 

to seasonal adjustment.

Exhibit 1 shows the type, year, and month of experimental outlier regressors for all BLS seasonally adjusted industries. If the ramp identified on the basis of the peak and 

trough of an industry had a t-statistic greater than 3.5, 

then the ramp was used in the experimental treatment to 

remove the decline due to the recession. In addition, the 

X-12-ARIMA software selected any outliers found with a 

t-statistic greater than 3.5. The figure 3.5 is the optimal 

critical value routinely used to detect outliers.

Experimental treatment of nonfarm employment

To measure a quantity’s growth over time, the cumulative 

change in the quantity is commonly used, beginning at a 

point in time. Accordingly, in what follows, the cumulative change in employment beginning in the fourth quarter of 2011 through the first quarter of 2012 is compared 

for the original and the experimental series. The concern 

is that removing the impact of the recession, particularly 

the steep declines that took place in the months making 

up the fourth quarter of 2008 through the months constituting the first quarter of 2009, would result in a significant shift in employment growth from the former period to the latter. The cumulative change in employment 

beginning in the second quarter of 2011 and running 

through the third quarter of that year also is compared for 

the original and the experimental series, in order to determine whether there was a significant shift in employment 

growth as a result of removing the impact of the recession. At the time of this analysis, the final employment 

estimates for the third quarter of 2012 were not available; 

therefore, the cumulative change from the second quarter 

of 2011 through the third quarter of the same year is used 

for comparison.

Chart 2 compares the month-to-month changes in total 

nonfarm employment from the original seasonally adjusted employment series with those from the experimental 

seasonally adjusted employment series with the decline 

due to the recession removed prior to seasonal adjustment. From the second through the third quarter of 2011, 

the cumulative change of the original series was 892,000, 

compared with 916,000 for the experimental series, a 

difference of 24,000. From the fourth quarter of 2011 

through the first quarter of 2012, the cumulative monthto-month change of the original series was 1.106 million, 

compared with 1.087 million for the experimental series, 

a difference of 19,000. Removing the decline due to the 

recession results in an increase of 24,000 in the cumulative 

change from the second quarter of 2011 through the third 

quarter of that year and a decline of 19,000 in the cumulative change from the fourth quarter of 2011 through 

the first quarter of 2012. The shift in the distribution of 

cumulative employment change across quarters does not 

alter the pattern of stronger employment increases from 

the fourth through the first quarter and weaker employment increases from the second through the third quarter. 

The overall trend is consistent between the original and 

experimental series. Following the standard procedure 

for calculating seasonally adjusted total nonfarm employment, the experimental series is aggregated from 158 directly adjusted series. The remainder of this article gives 

examples of several of the directly adjusted series. 

Residential remodelers

Employment declines in construction began before the 
Monthly Labor Review • October 2012  45

See footnote at end of table.

Exhibit 1. Experimental outlier regressors for BLS seasonally adjusted industries, t–statistic > 3.5

Industry

Type, year, and month of regressor

Ramp

(beginning–end) Automatically identified outliers

Logging None TC2005.04, LS2009.03

Oil and gas extraction RP2008.12–2009.12 AO2008.04

Coal mining RP2009.01–2009.12 None 

Metal ore mining RP2008.10–2009.10 AO2003.06, AO2008.12

Nonmetallic mineral mining and quarrying RP2007.06–2010.05 TC2008.05

Support activities for mining RP2008.09–2009.10 None 

New single-family general contractors RP2006.04–2011.07 AO2002.11, AO2003.05, LS2009.01

New multifamily general contractors RP2006.06–2011.09 None

New housing operative builders RP2006.12–2012.02 TC2004.06

Residential remodelers RP2006.10–2010.02 LS2009.03

Industrial building RP2008.04–2011.05 None 

Commercial building RP2008.03–2010.09 AO2005.01, AO2006.07, AO2009.05

Heavy and civil engineering construction RP2007.06–2010.02 TC2005.06, AO2005.12, AO2007.02, LS2009.04,

LS2010.12, LS2012.05

Residential specialty trade contractors RP2006.02–2010.12 None

Nonresidential specialty trade contractors RP2008.01–2010.06 AO2007.02

Poured concrete structure contractors RP2006.04–2011.08 AO2007.02

Steel and precast concrete contractors RP2008.02–2010.11 None 

Framing contractors RP2005.11–2011.01 LS2009.01

Masonry contractors RP2006.08–2012.02 AO2007.02, LS2009.03

Glass and glazing contractors RP2008.02–2010.10 TC2003.06, AO2005.05

Roofing contractors RP2006.01–2010.02 None 

Siding contractors RP2006.03–2011.01 None 

Other building exterior contractors RP2008.02–2010.12 None 

Electrical contractors RP2007.06–2010.11 None 

Plumbing and HVAC contractors RP2007.07–2010.06 None 

Other building equipment contractors RP2008.04–2010.03 LS2003.03

Drywall and insulation contractors RP2006.08–2010.09 None 

Painting and wall covering contractors RP2006.05–2011.01 None 

Flooring contractors RP2007.05–2012.01 LS2009.02

Tile and terrazzo contractors RP2006.08–2012.02 None 

Finish carpentry contractors RP2006.04–2011.04 LS2009.02

Other building finishing contractors RP2006.09–2010.08 None 

Site preparation contractors RP2007.01–2011.04 TC2008.10

All other specialty trade contractors RP2006.04–2010.05 TC2005.01, AO2005.11

Wood products RP2006.02–2011.07 AO2009.02

Nonmetallic mineral products RP2006.04–2011.10 TC2008.10

Primary metals RP2008.09–2009.07 LS2008.10, LS2009.07

Fabricated metal products RP2008.09–2010.01 AO2009.01

Machinery RP2008.12–2010.01 AO2005.10

Computer and peripheral equipment RP2008.11–2009.04 LS2003.01, LS2006.01, LS2007.01, LS2009.05

Communications equipment None  AO2005.01, TC2011.02

Audio and video equipment None  AO2002.05, TC2011.05

Semiconductors and electronic components None  TC2007.01

Electronic instruments None  TC2003.01, LS2007.03

Magnetic media manufacturing and reproduction None  LS2002.12, LS2004.06, TC2007.08

Electrical equipment and appliances RP2008.07–2010.01 TC2009.04

Transportation equipment RP2008.07–2009.06 LS2009.01, TC2009.02

Motor vehicles and parts RP2008.01–2009.06 AO2009.01, LS2009.01, TC2009.05

Furniture and related products None  LS2003.04

Miscellaneous manufacturing RP2008.11–2010.06 None 

Food manufacturing None  None 

Beverages and tobacco products RP2008.04–2010.07 TC2004.11, TC2011.01

Textile mills RP2008.01–2010.01 AO2010.01

Textile product mills None  TC2003.08, LS2009.03

Apparel None  AO2009.06

Leather and allied products RP2008.09–2010.04 None 
CES Seasonal Adjustment

46  Monthly Labor Review • October 2012

See footnote at end of table.

Paper and paper products RP2008.07–2009.04 None 

Printing and related support activities None  AO2011.08

Petroleum and coal products RP2008.07–2011.08 TC2007.07, TC2009.12, TC2011.01

Chemicals RP2008.07–2011.01 LS2009.11

Plastics and rubber products RP2008.07–2009.10 LS2009.01

Durable goods None  None 

Nondurable goods RP2008.01–2010.09 None 

Electronic markets and agents and brokers RP2008.02–2010.01 None 

Automobile dealers RP2008.06–2009.11 LS2008.09, TC2008.09

Other motor vehicle dealers RP2008.03–2010.01 None 

Auto parts, accessories, and tire stores RP2007.02–2009.03 AO2002.01

Furniture and home furnishings stores RP2006.06–2010.08 LS2007.11

Electronics and appliance stores RP2008.04–2009.11 TC2009.03

Building material and garden supply stores RP2006.09–2010.11 LS2009.03

Food and beverage stores RP2008.03–2010.06 None 

Health and personal care stores RP2008.01–2010.12 TC2002.11, AO2005.09, LS2006.01, TC2009.01

Gasoline stations RP2008.01–2010.03 None 

Clothing and clothing accessories stores RP2007.11–2010.09 TC2007.11, LS2012.01

Sporting goods, hobby, book, and music stores RP2008.01–2012.01 TC2004.09, TC2009.10, TC2011.12

Department stores RP2008.01–2009.12 TC2002.04, LS2003.08, LS2003.11, LS2007.01, AO2012.01

Other general merchandise stores RP2009.05–2009.12 AO2006.03, AO2007.03

Miscellaneous store retailers RP2008.01–2010.12 AO2011.07

Nonstore retailers RP2007.12–2010.01 AO2003.12, LS2008.12, TC2010.01

Air transportation RP2008.03–2009.04 LS2003.04,TC2004.01, AO2006.11,TC2007.02, AO2007.05

Rail transportation RP2007.03–2009.12 AO2002.04, AO2002.06, LS2002.11, AO2003.08,

AO2008.06, TC2008.10, TC2009.01, LS2009.05,

TC2009.06, LS2011.02

Water transportation RP2008.07–2010.02 LS2004.08, AO2010.03

Truck transportation RP2007.01–2010.03 None 

Transit and ground passenger transportation RP2008.08–2009.09 LS2002.07, LS2002.09, AO2009.06, AO2012.04

Pipeline transportation RP2009.10–2010.11 LS2008.05, LS2009.09

Scenic and sightseeing transportation None  AO2004.10, TC2007.01, LS2011.05

Support activities for transportation RP2008.08–2010.02 None 

Couriers and messengers None  TC2006.10, AO2008.11, AO2009.12, AO2011.11

Warehousing and storage RP2008.04–2010.01 None 

Utilities RP2009.02–2010.09 None 

Publishing industries, except Internet RP2008.07–2010.01 None 

Motion picture and sound recording industries None  None 

Broadcasting, except Internet RP2008.11–2011.11 None 

Telecommunications None  LS2002.12

Data processing, hosting and related services RP2007.07–2010.08 None 

Other information services None  None 

Monetary authorities—central bank RP2008.09–2011.04 LS2004.05, TC2007.05, AO2007.07, LS2008.10, LS2011.12

Depository credit intermediation RP2007.09–2010.08 TC2007.04

Commercial banking RP2008.04–2010.06 AO2006.01, TC2007.04

Nondepository credit intermediation RP2005.11–2010.06 AO2007.08, LS2007.08, LS2009.04

Activities related to credit intermediation RP2006.05–2010.04 None 

Securities, commodity contracts, investments RP2008.08–2010.03 AO2010.09

Insurance carriers and related activities RP2008.03–2010.03 None 

Funds, trusts, and other financial vehicles RP2008.11–2011.10 LS2005.01, TC2005.04, AO2011.07

Real estate RP2007.05–2010.07 None 

Rental and leasing services RP2005.03–2011.06 None 

Lessors of nonfinancial intangible assets None  LS2005.04

Legal services RP2007.05–2010.06 LS2005.09

Accounting and bookkeeping services RP2008.01–2010.10 TC2002.05, AO2002.12, AO2003.02, AO2010.11,

LS2011.05

Architectural and engineering services RP2008.02–2010.09 None 

Exhibit 1. Experimental outlier regressors for BLS seasonally adjusted industries, t–statistic > 3.5—Continued

Industry

Type, year, and month of regressor

Ramp

(beginning–end) Automatically identified outliers
Monthly Labor Review • October 2012  47

Specialized design services RP2008.01–2010.06 None 

Computer systems design and related services None  TC2002.07, AO2002.12, LS2003.07, LS2004.04,

TC2006.01, LS2006.11

Management and technical consulting services RP2008.09–2010.05 TC2002.08

Scientific research and development services RP2008.10–2009.07 AO2007.09, LS2008.02

Advertising and related services RP2007.09–2010.03 LS2003.07, TC2004.07, TC2008.10

Other professional and technical services RP2008.04–2009.10 LS2006.07, AO2008.01, AO2009.10

Management of companies and enterprises RP2008.08–2009.12 TC2009.01

Office administrative services RP2008.05–2009.05 AO2002.07, TC2006.11

Facilities support services RP2007.12–2012.02 None 

Employment services RP2006.08–2009.08 None 

Temporary help services RP2006.08–2009.08 None 

Business support services RP2008.11–2010.04 TC2004.06, LS2005.10, LS2006.01

Travel arrangement and reservation services RP2007.07–2010.09 TC2005.10, LS2008.11, LS2009.02

Investigation and security services RP2008.07–2010.04 AO2005.11, AO2008.11, AO2009.02

Services to buildings and dwellings RP2007.12–2010.03 LS2002.04, AO2005.11, AO2009.05, AO2010.01

AO2010.03, TC2012.03

Other support services RP2007.10–2010.01 AO2002.11

Waste management and remediation services RP2008.01–2009.06 AO2003.07, TC2004.01

Educational services None  AO2004.09

Offices of physicians None  None 

Offices of dentists RP2008.11–2009.12 None 

Offices of other health practitioners None  None 

Outpatient care centers None  None 

Medical and diagnostic laboratories None  AO2007.07, LS2008.10, TC2010.03

Home health care services None  None 

Other ambulatory health care services None  None 

Hospitals None  LS2003.07

Nursing care facilities RP2003.06–2004.02 LS2011.11

Residential mental health facilities None  LS2007.06

Community care facilities for the elderly None  TC2005.09, AO2007.06

Other residential care facilities None  LS2009.04

Individual and family services None  None 

Emergency and other relief services RP2004.08–2005.07 AO2002.07

Vocational rehabilitation services RP2007.10–2011.03 TC2006.05

Child daycare services RP2008.12–2012.02 TC2002.06

Performing arts and spectator sports None  LS2010.10

Museums, historical sites, and similar institutions RP2008.05–2010.10 None 

Amusements, gambling, and recreation RP2008.02–2010.01 AO2009.09

Accommodation RP2008.02–2010.02 TC2002.07

Food services and drinking places RP2007.12–2010.02 LS2009.05

Repair and maintenance RP2007.05–2010.02 None 

Personal and laundry services RP2008.09–2010.08 TC2006.01

Membership associations and organizations RP2008.10–2011.07 None 

Federal, except U.S. Postal Service None  LS2003.04, LS2003.10, AO2003.11, AO2004.04,

TC2005.12, LS2010.05

U.S. Postal Service None  TC2002.05, TC2002.07, TC2006.07, LS2008.01,

AO2008.12, AO2009.07, AO2009.12, LS2010.02

State government education None  TC2002.02, LS2002.09, AO2009.07

State government, excluding education None  AO2011.09

Local government education None  AO2003.03,AO2003.05,AO2003.07, LS2003.09, LS2004.03,

LS2005.06,TC2005.10, LS2006.01, LS2006.05, LS2006.09,

AO2007.07, LS2007.12,TC2008.07, LS2008.10, AO2009.11,

LS2010.09, AO2011.04, AO2011.06, AO2011.08

Local government, excluding education None  TC2009.07

NOTE: AO = additive outlier; LS = level shift; RP = ramp; TC = temporar

change.

Exhibit 1. Experimental outlier regressors for BLS seasonally adjusted industries, t–statistic > 3.5—Continued

Industry

Type, year, and month of regressor

Ramp

(beginning–end) Automatically identified outliers

SOURCE:  U.S. Bureau of Labor Statistics.
CES Seasonal Adjustment

48  Monthly Labor Review • October 2012

Month-to-month change in total nonfarm seasonally adjusted employment, original series (including 

2007–2009 recession) and experimental series (excluding 2007–2009 recession), January 2010 to June 

2012

Chart 2.

Thousands Thousands

SOURCE: U.S. Bureau of Labor Statistic

600

500

400

300

200

100

0

–100

–200

600

500

400

300

200

100

0

–100

–200

Original Experimental

Chart 3. Month-to-month change in residential remodelers seasonally adjusted employment, original series 

(including 2007–2009 recession) and experimental series (excluding 2007–2009 recession), January 

2010 to June 2012

Thousands Thousands

8

6

4

2

0

–2

–4

–6

8

6

4

2

0

–2

–4

–6

SOURCE: U.S. Bureau of Labor Statistic

Original Experimental

 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May 

 2010 2011 2012

 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May 

 2010 2011 2012
Monthly Labor Review • October 2012  49

2007–2009 recession for most industries in this sector. 

For residential remodelers, employment reached its peak 

in late 2006 and its trough in early 2010. A ramp for 

this period was used to remove the impact of the decline 

due to the recession prior to seasonal adjustment. Chart 

3 compares the month-to-month changes in residential 

remodelers from the original seasonally adjusted employment series with those from the experimental seasonally 

adjusted employment series with the decline due to the 

recession removed prior to seasonal adjustment. From 

the second quarter of 2011 through the third quarter of 

that year, the cumulative change in the original series was 

3,100, compared with 3,900 for the experimental series, a 

difference of less than a thousand. From the fourth quarter of 2011 through the first quarter of 2012, the cumulative change in the original series was 8,200, compared 

with 7,500 for the experimental series, a difference of less 

than a thousand.

Electronic and appliance stores

Employment declines in retail began close to the 2007–

2009 recession for most industries in this sector. For 

electronic and appliance stores, employment reached its 

peak in early 2008 and its trough in late 2009. A ramp for 

this period was used to remove the impact of the decline 

due to the recession prior to seasonal adjustment. Chart 

4 compares the month-to-month changes in electronic 

and appliance stores from the original seasonally adjusted employment series with those from the experimental 

seasonally adjusted employment series with the decline 

due to the recession removed prior to seasonal adjustment. From the second quarter of 2011 through the third 

quarter of that same year, the cumulative change in the 

original series was –12,700, compared with –11,600 for 

the experimental series, a difference of 1,100. From the 

fourth quarter of 2011 through the first quarter of 2012, 

the cumulative change in the original series was –8,200, 

compared with –9,100 for the experimental series, a difference of less than a thousand.

Truck transportation

Employment declines in transportation began close to 

the 2007–2009 recession for most industries in this sector. 

For truck transportation, employment reached its peak 

Chart 4. Month-to-month change in electronic and appliance stores seasonally adjusted employment, original

series (including 2007–2009 recession) and experimental series (excluding 2007–2009 recession), 

January 2010 to June 2012

 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May 

 2010 2011 2012

Original Experimental

Thousands Thousands

SOURCE: U.S. Bureau of Labor Statistic

10

8

6

4

2

0

–2

–4

–6

–8

–10

10

8

6

4

2

0

–2

–4

–6

–8

–10
CES Seasonal Adjustment

50  Monthly Labor Review • October 2012

in early 2007 and its trough in early 2010. A ramp for 

this period was used to remove the impact of the decline 

due to the recession prior to seasonal adjustment. Chart 

5 compares the month-to-month changes in truck transportation from the original seasonally adjusted employment series with those from the experimental seasonally 

adjusted employment series with the decline due to the 

recession removed prior to seasonal adjustment. From 

the second quarter of 2011 through the third quarter of 

that same year, the cumulative change in the original series was 14.9 thousand, compared with 16.4 thousand for 

the experimental series, a difference of 1,500. From the 

fourth quarter of 2011 through the first quarter of 2012, 

the cumulative change in the original series was 27,900, 

compared with 26,500 in the experimental series, a difference of 1.4 thousand.

Temporary help services

The beginning of the employment declines in professional 

and business services varied across industries in this sector. For temporary help services, employment reached its 

peak in mid-2006 and its trough in mid-2009. A ramp for 

this period was used to remove the impact of the decline 

due to the recession prior to seasonal adjustment. Chart 

6 compares the month-to-month changes in temporary 

help services from the original seasonally adjusted employment series with those from the experimental seasonally adjusted employment series with the decline due to 

the recession removed prior to seasonal adjustment. From 

the second quarter of 2011 through the third quarter of 

that year, the cumulative change in the original series was 

48,900, compared with 44,600 in the experimental series, 

a difference of 4,300. From the fourth quarter of 2011 

through the first quarter of 2012, the cumulative change 

in the original series was 128,200, compared with 131,400 

for the experimental series, a difference of 3,200. In contrast to the other industries presented, the shift in employment across quarters for this industry moves in the 

opposite direction: removing the impact of the decline 

due to the recession results in a decrease in the cumulative change from the second quarter of 2011 through the 

third quarter of that year and an increase in the cumulative 

change from the fourth quarter of 2011 through the first 

quarter of 2012.

AFTER REMOVAL OF THE DECLINES due to the 2007–

2009 recession prior to seasonal adjustment, the seasonChart 5.

14

12

10

8

6

4

2

0

–2

–4

–6

Thousands Thousands

14

12

10

8

6

4

2

0

–2

–4

–6

Month-to-month change in truck transportation seasonally adjusted employment, original series 

(including 2007–2009 recession) and experimental series (excluding 2007–2009 recession), January 

2010 to June 2012

SOURCE: U.S. Bureau of Labor Statistic

Original Experimental

 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May 

 2010 2011 2012
Monthly Labor Review • October 2012  51

Chart 6.

SOURCE: U.S. Bureau of Labor Statistic

Month-to-month change in temporary help services seasonally adjusted employment, original

series (including 2007–2009 recession) and experimental series (excluding 2007–2009 recession), 

January 2010 to June 2012

Original Experimental

Thousands Thousands

60

50

40

30

20

10

0

–10

–20

60

50

40

30

20

10

0

–10

–20

ally adjusted month-to-month changes in employment 

from the experimental series show no significant difference from those of the original series. In addition, the pattern of stronger increases in employment from the fourth 

quarter of one year through the first quarter of the next 

and weaker increases from the second through the third 

quarter of the same year has persisted since 2011, even 

after the influence of the declines due to the recession is 

removed. CES employment data are not treated with additional interventions over and above the standard procedure, because that procedure produces accurate seasonally 

adjusted estimates. Also, it is important to note that the 

experimental treatment presented in this article cannot 

be applied concurrently to the most recent data in real 

time: the additional types of outlier can be applied only 

retrospectively, after reviewing historical data. The X12-ARIMA seasonal adjustment method, along with the 

concurrent update of seasonal factors, continues to provide accurate seasonally adjusted estimates and adapts to 

evolving changes in trends or seasonal patterns without 

allowing extreme changes to be absorbed into the seasonal component.

Notes

1 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 

Economic Statistics, vol. 16, no. 2, 1998, pp. 127–152.

2 Jurgen Kropf, Christopher Manning, Kirk Mueller, and Stuart 

Scott, Concurrent Seasonal Adjustment for Industry Employment Statistics

(U.S. Bureau of Labor Statistics, 2002). 

3 Nathan Clausen, “Benchmark Article: BLS Establishment Estimates Revised to Incorporate March 2011 Benchmarks” (U.S. Bureau 

of Labor Statistics, 2012). 

4 Demetra Lytras, Modeling Recession Effects (U.S. Census Bureau, 2012).

5 Gerhard Bry and Charlotte Boschan, Cyclical Analysis of Time 

Series: Selected Procedures and Computer Programs (Cambridge, MA, 

National Bureau of Economic Research, 1971).

 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May 

 2010 2011 2012
CES Seasonal Adjustment

52  Monthly Labor Review • October 2012

APPENDIX A. Basic time series decomposition

Non-seasonally-adjusted series

Multiplicative:

Observed = Trend × Seasonal × Irregular,

or

O = TSI.

Additive:

Observed = Trend + Seasonal + Irregular,

or

O = T + S + I.

Seasonally adjusted series (SA)

Multiplicative:

SA = O = TI.

Additive:

SA = O _ S = T + I.

In the preceding equations,

Observed (O) = the original time series,

Trend (T) = the long-term progression of the time series combining the trend and business cycle,

Seasonal (S) = the within-year fluctuations, monthly or quarterly, that are repeated every year, and

Irregular (I) = the short-term random or erratic fluctuations that are not covered by the other components.

S
Monthly Labor Review • October 2012  53

Additive outliers (AO) 

Series shifts at a single point in time (t): 

�

� ��� � � ��

� ��� � � ��

 

Level shifts (LS) 

Series shifts suddenly and then continues at new level: 

�

�� ��� � � ��

� ��� � � ��

Ramps (RP) 

Series is at one level, slowly shifts to another, and continues at the new level: 

�

�� ��� � � ��

�� � ��� �� ⁄ �

� ��� � � ��

� ��� � � ��� �� �����

Temporary changes (TC) 

Series shifts suddenly and then declines slowly to original level: 

� � ��� � � ��

����� ��� � � ��

 

APPENDIX B. X-12-ARIMA types of outlier