Seasonality in Regression

Christopher A. Sims
1974 Journal of the American Statistical Association  
Recent work by D. Grether and M. Nerlove (1.970) and by H. M. Rosenblatt (1.968) among others has addressed again the old question of how best to seasonally adjust economic time series. This work has not, however, considered the question of how seasonal ad,justment ar the failure to ad.iust series contaminated by seasonal noise might affect analysis of re:ations between series. other recent work which has dealt wi th seasonality in regression models (J. J. Thomas and Kenneth F. It/allis (1971),
more » ... F. It/allis (1971), D. Jorgenson (1964), M. C. Lovell (1.963» has given specific guidance only for narrower definitions of seasonali ty than that now commonly used in considering seasonal adjustment of individual series. V TIlts paper develops useful results for regression in the presence of seasonal noise which evolves slowly, producing sharp but not infinitesimally narrow peaks at seasonal frequencies in the spectral densities af the variables. V The paper's analytical parts assume the reader is familiar ",ith the theory of covariance-stationary stochastic processes, though at some points there is an attempt to recapitulate briefly in less technical language. A bivariate distributed lag model is the basis for discussion throughout. Extensions to multivariate distributed Jag regressions are obvious, and time series regression models in which no lags appear are a special case of the pa.per' s general distributed Jag mode L.
doi:10.2307/2285991 fatcat:btg52xfykze7dhqtbodsa2gquy