Seasonal Adjustment of Economic Time Series and Multiple Regression Analysis

Abstract The logical implications of certain simple consistency requirements for appraising alternative procedures for seasonal adjustment constitute the first problem considered in this paper. It is shown that any sum preserving technique of seasonal adjustment that satisfies the quite reasonable requirements of orthogonality and idempotency can be executed on the electronic computer by standard least squares regression procedures. Problems involved in utilizing seasonally adjusted data when estimating the parameters of econometric models are examined. Extending the fundamental Frisch-Waugh theorem concerning trend and regression analysis to encompass problems of seasonality facilitates the comparison of the implications of running regressions on data subjected to prior seasonal adjustment with the effects of including dummy variables with unadjusted data. Complicated types of moving seasonal patterns that may be handled by the dummy variable procedure are considered. Although efficient estimates of the parameters of the econometric model may be obtained in appropriate circumstances when data subjected to prior seasonal adjustment by the least squares procedure are employed, there is an inherent tendency to overstate the significance of the regression coefficients; a correction procedure is suggested. When seasonally adjusted data are employed, certain special complications must be taken into account in applying Aitken's generalized least squares procedure in order to deal with autocorrelated residuals. The entire argument extends to two-stage least squares estimation of the parameters of simultaneous equation models.