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It is sometimes assumed that the R 2 of a regression of a first-order differenced time series on seasonal dummy variables reflects the amount of seasonal fluctuations that can be explained by deterministic variation in the series. In this paper we show that neglecting the presence of seasonal unit roots may yield spuriously high values of this coefficient.

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The first author would like to acknowledge the financial support of the SSHRC and NSERC of Canada. as well as the Fonds FCAR of ~bee. Part of this paper was done while the first author was on sabbatical leave at the Cowles Foundation, Yale University. Its financial support and hospitality are also gratefully acknowledged.The third author is grateful for the hospitality of the University of California, San Diego where he was a visiting scholar during the spring of 1991, to Wilfrid Laurier University for financial support through a short-term research grant. ABSTRACTIt is well known that misspecification of a trend leads to spurious cycles in detrended data '.:(see, e.g., Nelson and Kang (1981)). SeasonaJadjustmentproceduresmakeassumptions, either• 'Implicitly or explicitly, about roots on the unit circle both at the zero and seasonal frequencies.Consequently, seasonal adjustment procedures may produce spurious detrending and other : statistically undesirable effects.In this paper, we document, for a large class of widely used U.S. quarterly macroeconomic , series, the effects of competing seasonal adjustment procedures on the univariate time series 'properties of adjusted series. We also investigate which procedures are most appropriate, given the properties of the data. Overaff, we find very significant cflfferences and evidence of spurious , cycles among series filtered via different adjustment procedures. A byproduct of our paper is. . an extension of data-dependent model selection rules in ADF tests, proposed and analyzed by Hall (1990) (1979), Bell and Hillmer (1984) and Hylleberg (1986) for surveys and detailed discussion). As is now well known, many time series are ncinstationary and they are widely believed to contain a unit root at the zero frequency (see CampbeU and Perron 1991 for a recent survey). Similarly, usual seasonal adjustment procedures make either implicitly or explicitly assumptions about roots on the unit circle both at the zero as wen as at the seasonal frequency and its harmonics. TypicaUy. in applied research, adjustment for seasonality assumes that seasonality is deterministic and can be removed via seasonal dummies thus ignoring the possibility ol the stochastic and nonstationary nature of seasonality. On the other hand, the commonly applied monthly Census X· 11 program, for instance, implies dala transformations which include the (1 + L + L 2 + .... + L 11 , where L 1 , is the lag operator for I periods) filter, resulting in a •removar of unit roots at the monthly seasonal frequency and its harmonics. 1Data transformations thal go along with the removal of seasonals may or may not be approprlale, just like trend removal can be inadequately done. In this paper we document for a large class of quarterly U.S. Post World War II time series how several of the data transformations typically associated with seasonal adjustment affect the univariate time series properties of interest to economists. such as the autocorrelation and partial autocorrelation functions of the transformed data. ...