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 perceptive.

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 runâ€”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 projected factors.

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 components difficult.

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 not known.

Footnotes^{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
1978.

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,
1988.

Dagum, Estela Bee.* The X-11 ARIMA Seasonal Adjustment Method.
*Ottawa, Statistics Canada, January 1983 (Statistics Canada Catalogue
No. 12-564E).

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

**Last Modified Date: **February 18, 2014