Seasonal Adjustments in the NBER Macrohistory Data

Many of the time series in the nber collection contain a seasonally adjusted series as well as the original data. Dr. Geoffrey H. Moore, Director of Business Cycle Research at NBER, has written the following remarks on the subject of seasonal adjustments:

The monthly and quarterly data in the National Bureau's collection of time series are adjusted, in most instances, for seasonal variations. Virtually the only exceptions are series where no seasonal variation was present or could be found. Occasionally seasonal movements will disappear from a series for a period of years, as for example when prices are fixed by fiat or when the monetary authorities counter the seasonal pressures on interest rates. The pervasiveness of seasonal variations can be traced to their source: recurring changes in the weather or climatic conditions and conventional changes due to religious observances, holidays, and other customs, the number of days in the month, legal conditions such as tax payment dates, or business practices such as quarterly payment of dividends. For purposes of business cycle analysis the repetitive movements caused by these factors are largely irrelevant and confusing. They are removed by seasonal adjustment.

Only the original and the seasonally adjusted data are reproduced in this file. The seasonal factors used to derive the seasonally adjusted data are not shown. They can be reproduced, at least approximately, in most instances, by dividing the original data by the seasonally adjusted. In some instances, notably where the original data have plus and minus values, the seasonally adjusted figures should be subtracted from the original to derive the seasonal factors. since the seasonal factors change from time to time, sometimes every year, it may not be easy to reproduce the factors precisely, because of rounding problems. Moreover, the method of estimating the seasonal factors has not been specified. The original files from which these records were taken usually contain worksheets which show how the seasonal factors were estimated. Most of the series were adjusted by the National Bureau and a variety of methods were used, which will be briefly described here. For further details the user is referred to the sources listed below.

Methods of seasonal adjustment used by the National Bureau changed during the period, beginning in the 1920's when the data were being collected and analyzed. The two principal methods used were the "monthly means" method and the "ratio to moving average method." With the monthly means method the original data for all the Januaries were averaged over a period of, say, ten years, then the mean of all the Februaries was obtained, and so on. These twelve averages are then adjusted for secular trend and expressed as a ratio to the average for the year. The resulting ratios for January, February, etc. are the seasonal factors to be divided into the original data to obtain the seasonally adjusted data for the ten year period. Variations on this method involved taking averages of the middle items in the array of januaries, etc.; applying the seasonal indexes to a period shorter or longer than the period from which they were derived; and operating with differences instead of ratios.

The ratio to moving average method relies on the principle that a twelve month moving average is not, as a rule, affected by seasonal variations but does contain all of the secular trend, much of the cyclical movement, and little of the irregular fluctuation. Hence when it is divided into the original data the ratios contain all of the seasonal variation, none of the trend, some of the cyclical movement and all of the irregular. By averaging all the January ratios for a period of, say, seven years, then all the February ratios, etc., one obtains a set of seasonal indexes in which the residual cyclical and irregular movements have largely canceled out. Variants of this method involved using weighted moving averages instead of a simple twelve month average, altering the periods over which the ratios were averaged or altering the method of averaging, and using differences instead of ratios. This method became the basis for the widely used electronic computer method of seasonal adjustment developed by Julius Shiskin, varously called X-11, Census method II, etc. A number of the series in the bureau's collection were adjusted by the computer program.

The ratio to moving average method is readily adapted to producing a moving seasonal adjustment, i.e. seasonal factors that change every year in a smooth, progressive fashion. another method used to adjust the seasonal factors from one year to another is called amplitude adjustment: the pattern of the factors during the year is held constant but the size of the seasonal swing is made larger in some years than in others by means of a regression adjustment. Many series have been adjusted, usually by the compilers, by an implicit moving seasonal. Seasonally adjusted components are summed to form the total, and shifts in their magnitudes cause changes in the implicit seasonal adjustment of the total. Finally, in some instances a special method, devised by Arthur F. Burns, for eliminating seasonal variations from highly irregular series has been used. It involves multiplying the seasonal factors (expressed as deviations from 100) by a smoothed version of the series (a twelve-month moving average) and subtracting the resulting products from the original data. The method assumes that the absolute amount by which the series sould be adjusted (i.e., in original units) is independent of the irregular component of the series.

For fuller explanations and illustrations of the methods of seasonal adjustment used by the national bureau over the years consult the following nber publications:

Notes on sources

Approximately half the data presented in the construction datasets was published in Source Book of Statistics Relating to Construction, by Robert E. Lipsey and Doris Preston (New York: National Bureau of Economic Research, 1966). This work included extensive documentation of sources. This documentation is presented here in abridged form. if further information is necessary, the original work contains additional information in many instances.

Readers of this document should remember that the NBER web site at does not include the seasonally adjusted series if an unadjusted series is available. This was done in view of the increased interest of researchers in doing their own seasonal adjustment, and because proofreading the adjusted series also would have been quite costly. Last modified 13 September 2000.