On the (Mis)Specification of Seasonality and its Consequences: An Empirical Investigation with US Data

Abstract

It is well known that mis-specification of a trend leads to spurious cycles in detrended data (see, e.g., Nelson and Kang (1981)). Seasonal-adjustment procedures make assumptions, either implicitly or explicitly, about roots on the unit circle both at the zero and seasonal frequencies. Consequently, seasonal-adjustment procedures may produce spurious seasonal variation and other statistically undesirable effects. In this paper we document for a large class of widely used US quarterly macroeconomic series the effects of competing seasonal-adjustment procedures on the univariate time-series properties of the adjusted series. We also investigate which procedures are most appropriate given the properties of the data. Overall, we find very significant differences and evidence that several U.S. macroeconomic time series contain a mixture of deterministic and stochastic seasonal components.

The first author would like to acknowledge the financial support of the SSHRC and NSERC as well as the Fonds FCAR of Quebec. 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 is 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, a Course Remission Grant, and the Academic Development Fund. Comments by anonymous referees on earlier drafts helped improve the paper considerably. A companion C.R.D.E. (Université de Montréal) working paper with a more detailed account of the empirical results is available on request.