Issues Involved With the Seasonal Adjustment of Economic Time Series

In the first part of this article, we briefly review the history of seasonal adjustment and statistical time series analysis in order to understand why seasonal adjustment methods have evolved into their present form. This review provides insight into some of the problems that must be addressed by seasonal adjustment procedures and points out that advances in modern time series analysis raise the question of whether seasonal adjustment should be performed at all. This in turn leads to a discussion in the second part of issues invloved in seasonal adjustment. We state our opinions about the issues raised and renew some of the work of our authors. First, we comment on reasons that have been given for doing seasonal adjustment and suggest a new possible justification. We then emphasize the need to define precisely the seasonal and nonseasonal components and offer our definitions. Finally, we discuss our criteria for evaluating seasonal adjustments. We contend that proposed criteria based on empirical comparisons of estimated components are of little value and suggest that seasonal adjustment methods should be evaluated based on whether they are consistent with the information in the observed data. This idea is illustrated with an example.

[1]  On the Laws of the Currency in Ireland, as Exemplified in the Changes that Have Taken Place in the Amount of Bank Notes in Circulation in Ireland, Since the Passing of the Act of 1845 , 1852 .

[2]  Arthur Schuster,et al.  On the investigation of hidden periodicities with application to a supposed 26 day period of meteorological phenomena , 1898 .

[3]  G. Yule On the Time‐Correlation Problem, with Especial Reference to the Variate‐Difference Correlation Method , 1921 .

[4]  Mortality from Pulmonary Tuberculosis in Recent Years. 1. The Variation in Its Course during the War and Its Decline since 1918 , 1922 .

[5]  The Method of Monthly Means for Determination of a Seasonal Variation , 1922 .

[6]  W. Beveridge,et al.  Wheat Prices and Rainfall in Western Europe , 1922 .

[7]  Trade Forecasting and Prices , 1923 .

[8]  W. L. Crum The Use of the Median in Determining Seasonal Variation , 1923 .

[9]  Warren M. Persons,et al.  Correlation of Time Series , 1923 .

[10]  Cycles of Rates on Commercial Paper , 1923 .

[11]  Helen D. Falkner The Measurement of Seasonal Variation , 1924 .

[12]  Seasonal Variation as a Relative of Secular Trend , 1924 .

[13]  An Improved Method for Measuring the Seasonal Factor , 1924 .

[14]  Progressive Variation in Seasonality , 1925 .

[15]  On the Measurement of Seasonal Variation , 1925 .

[16]  G. Yule Why do we Sometimes get Nonsense-Correlations between Time-Series?--A Study in Sampling and the Nature of Time-Series , 1926 .

[17]  Methods of Computing Seasonal Indexes: Constant and Progressive , 1927 .

[18]  G. Yule On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers , 1927 .

[19]  Measurement of Variations in Seasonal Distribution , 1927 .

[20]  Oskar Anderson,et al.  On the Logic of the Decomposition of Statistical Series into Separate Components , 2022 .

[21]  Adjustments for the Influence of Easter in Department Stores Sales , 1927 .

[22]  The use of Moving Averages in the Measurement of Seasonal Variations , 1928 .

[23]  R. Fisher Tests of significance in harmonic analysis , 1929 .

[24]  The Variate Difference Method of Seasonal Variation , 1929 .

[25]  Frederick Robertson Macaulay,et al.  The Smoothing of Time Series , 1931 .

[26]  Seasonal Pattern and Seasonal Amplitude: Measurement of Their Short-Time Variations , 1932 .

[27]  Adjusting for the Changing Date of Easter in Economic Series , 1933 .

[28]  W. Ferger,et al.  Seasonal Variations in Industry and Trade. , 1934 .

[29]  Eugen Slutzky Summation of random causes as the source of cyclic processes , 1937 .

[30]  Horst Mendershausen,et al.  Annual Survey of Statistical Technique: Methods of Computing and Eliminating Changing Seasonal Fluctuations , 1937 .

[31]  Horst Mendershausen Eliminating Changing Seasonals by Multiple Regression Analysis , 1939 .

[32]  The variate difference method. , 1940 .

[33]  Dudley J. Cowden Moving Seasonal Indexes , 1942 .

[34]  A. Wald,et al.  On the Statistical Treatment of Linear Stochastic Difference Equations , 1943 .

[35]  Howard L. Jones Fitting Polynomial Trends to Seasonal Data by the Method of Least Squares , 1943 .

[36]  M. Kendall On the Analysis of Oscillatory Time-Series , 1945 .

[37]  M. Bartlett On the Theoretical Specification and Sampling Properties of Autocorrelated Time‐Series , 1946 .

[38]  P. Moran,et al.  Some theorems on time series. , 1947, Biometrika.

[39]  D. G. Champernowne,et al.  Sampling Theory Applied to Autoregressive Sequences , 1948 .

[40]  D. Cochrane,et al.  Application of Least Squares Regression to Relationships Containing Auto-Correlated Error Terms , 1949 .

[41]  Norbert Wiener,et al.  Extrapolation, Interpolation, and Smoothing of Stationary Time Series, with Engineering Applications , 1949 .

[42]  The decomposition of a series of observations composed of a trend, a periodic movement and a stochastic variable , 1949 .

[43]  M. Bartlett Periodogram analysis and continuous spectra. , 1950, Biometrika.

[44]  P. Whittle,et al.  TESTS OF FIT IN TIME SERIES , 1952 .

[45]  P. Whittle,et al.  Estimation and information in stationary time series , 1953 .

[46]  P. Whittle The Analysis of Multiple Stationary Time Series , 1953 .

[47]  P. Whittle A Statistical Investigation of Sunspot Observations with Special Reference to H. ALFVÉN'S Sunspot Model. , 1954 .

[48]  M. Kendall,et al.  A Study in the Analysis of Stationary Time-Series. , 1955 .

[49]  Harry Eisenpress Regression Techniques Applied to Seasonal Corrections and Adjustments for Calendar Shifts , 1956 .

[50]  Julius Shiskin,et al.  Electronic Computers and Business Indicators , 1957 .

[51]  J. Durbin EFFICIENT ESTIMATION OF PARAMETERS IN MOVING-AVERAGE MODELS , 1959 .

[52]  E. J. Hannan,et al.  THE ESTIMATION OF SEASONAL VARIATION , 1960 .

[53]  James Durbin,et al.  The fitting of time series models , 1960 .

[54]  J. Durbin Estimation of Parameters in Time‐Series Regression Models , 1960 .

[55]  Philip Solomon,et al.  Discussion of the Paper , 1961 .

[56]  A. M. Walker Large-sample estimation of parameters for movingaverage models , 1961 .

[57]  On Durbin's formula for the limiting generalized variance of a sample of consecutive observations from a moving-average process , 1961 .

[58]  L. Donald,et al.  of the INTERIOR , 1962 .

[59]  A. Yaglom,et al.  An Introduction to the Theory of Stationary Random Functions , 1963 .

[60]  A. M. Walker Large-sample estimation of parameters for autoregressive processes with moving-average residuals , 1962 .

[61]  E. J. Hannan,et al.  The Estimation of Seasonal Variation in Economic Time Series , 1963 .

[62]  M. Lovell Seasonal Adjustment of Economic Time Series and Multiple Regression Analysis , 1963 .

[63]  Dale W. Jorgenson,et al.  Minimum Variance, Linear, Unbiased Seasonal Adjustment of Economic Time Series , 1964 .

[64]  M. Nerlove SPECTRAL ANALYSIS OF SEASONAL ADJUSTMENT PROCEDURES , 1964 .

[65]  Norbert Wiener,et al.  Extrapolation, Interpolation, and Smoothing of Stationary Time Series , 1964 .

[66]  M. D. Godfrey,et al.  A spectrum analysis of seasonal adjustment , 1964 .

[67]  E. J. Hannan,et al.  The Estimation of a Changing Seasonal Pattern , 1964 .

[68]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[69]  M. Priestley Evolutionary Spectra and Non‐Stationary Processes , 1965 .

[70]  H. M. Rosenblatt Spectral analysis and parametric methods for seasonal adjustment of economic time series , 1965 .

[71]  Julius Shiskin,et al.  The X-11 variant of the census method II seasonal adjustment program , 1965 .

[72]  M. Lovell Alternative Axiomatizations of Seasonal Adjustment , 1966 .

[73]  R. C. Henshaw Application of the General Linear Model to Seasonal Adjustment of Economic Time Series , 1966 .

[74]  Eugene Sobel,et al.  Prediction of a noise-distorted, multivariate, non-stationary signal , 1967, Journal of Applied Probability.

[75]  M. D. Godfrey,et al.  Chapter 24. A Spectrum Analysis of Seasonal Adjustment , 1967 .

[76]  Michio Hatanaka,et al.  Chapter 26. A Theory of the Pseudospectrum and Its Application to Nonstationary Dynamic Econometric Models , 1967 .

[77]  E. J. Hannan Measurement of a wandering signal amid noise , 1967 .

[78]  D. Jorgenson Seasonal Adjustment of Data for Econometric Analysis , 1967 .

[79]  A. H. Young,et al.  Linear Approximations to the Census and BLS Seasonal Adjustment Methods , 1968 .

[80]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[81]  M. Nerlove,et al.  Some properties of "optimal" seasonal adjustment , 1970 .

[82]  E. J. Hannan,et al.  The Seasonal Adjustment of Economic Time Series , 1970 .

[83]  Eugene Sobel Approximate Best Linear Prediction of a Certain Class of Stationary and Nonstationary Noise-Distorted Signals , 1971 .

[84]  James A. Stephenson,et al.  Seasonal Adjustment of Economic Data by Application of the General Linear Statistical Model , 1972 .

[85]  M. Otto,et al.  Outliers in Time Series , 1972 .

[86]  K. Wallis Seasonal Adjustment and Relations Between Variables , 1974 .

[87]  Christopher A. Sims,et al.  Seasonality in Regression , 1974 .

[88]  E. Melnick,et al.  Filter design for the seasonal adjustment of a time series , 1974 .

[89]  George E. P. Box,et al.  Intervention Analysis with Applications to Economic and Environmental Problems , 1975 .

[90]  G. C. Tiao,et al.  Decomposition of Seasonal Time Series: A Model for the Census X-11 Program , 1976 .

[91]  Julius Shiskin Seasonal Adjustment of Sensitive Indicators , 1978 .

[92]  D. A. Pierce Seasonal adjustment when both deterministic and stochastic seasonality are present , 1978 .

[93]  William S. Cleveland,et al.  SABL: A Resistant Seasonal Adjustment Procedure with Graphical Methods for Interpretation and Diagnosis , 1978 .

[94]  Robert F. Engle,et al.  Estimating Structural Models of Seasonality , 1978 .

[95]  D. A. Pierce A Survey of Recent Developments in Seasonal Adjustment , 1980 .

[96]  G. Box,et al.  On a measure of lack of fit in time series models , 1978 .

[97]  Kenneth F. Wallis,et al.  Seasonal Adjustment and Multiple Time Series Analysis , 1978 .

[98]  Charles I. Plosser A Time Series Analysis of Seasonality in Econometric Models , 1978 .

[99]  Steven C. Hillmer,et al.  Analysis and Modeling of Seasonal Time Series , 1978 .

[100]  Michèle Hibon,et al.  Accuracy of Forecasting: An Empirical Investigation , 1979 .

[101]  L. Denby,et al.  Robust Estimation of the First-Order Autoregressive Parameter , 1979 .

[102]  G. Box,et al.  Bayesian analysis of some outlier problems in time series , 1979 .

[103]  Clive W. J. Granger,et al.  Seasonality: Causation, Interpretation, and Implications , 1979 .

[104]  Raphael Raymond V. BarOn,et al.  The Analysis of Single and Related Time Series Into Components: Proposals for Improving X-11 , 1979 .

[105]  Charles I. Plosser Short-term Forecasting and Seasonal Adjustment , 1979 .

[106]  David A. Pierce,et al.  Data revisions with moving average seasonal adjustment procedures , 1980 .

[107]  P. Newbold A NOTE ON RELATIONS BETWEEN SEASONALLY ADJUSTED VARIABLES , 1980 .

[108]  J. Burman Seasonal Adjustment by Signal Extraction , 1980 .

[109]  C. Granger,et al.  AN INTRODUCTION TO LONG‐MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING , 1980 .

[110]  David M. Grether,et al.  Analysis of Economic Time Series. A Synthesis. , 1980 .

[111]  H. Akaike SEASONAL ADJUSTMENT BY A BAYESIAN MODELING , 1980 .

[112]  E. Schlicht A Seasonal Adjustment Principle and a Seasonal Adjustment Method Derived From this Principle , 1981 .

[113]  Steven C. Hillmer,et al.  An ARIMA-Model-Based Approach to Seasonal Adjustment , 1982 .

[114]  J. Durbin,et al.  Local trend estimation and seasonal adjustment of economic and social time series (with discussion) , 1982 .

[115]  E. Robinson,et al.  A historical perspective of spectrum estimation , 1982, Proceedings of the IEEE.

[116]  Kenneth F. Wallis,et al.  Unobserved-Components Models For Seasonal Adjustment Filters , 1984 .

[117]  G. Kitagawa,et al.  A Smoothness Priors–State Space Modeling of Time Series with Trend and Seasonality , 1984 .

[118]  W. Bell,et al.  Signal Extraction for Nonstationary Time Series , 1984 .

[119]  Sandra K. McKenzie Concurrent Seasonal Adjustment with Census X-11 , 1984 .