Deterministic seasonal models and spurious regressions

Abstract

This paper examines the consequences of using seasonal dummies in regressions when seasonality is generated by seasonal unit roots. A unit root process can produce a deterministic seasonal pattern if the starting values contain a strong seasonal. It is shown, however, that subtraction of fixed seasonal means from a seasonally integrated series changes the covariance structure of the series, and often the means-subtracted series may take the appearance of a stationary series in small samples. Monte Carlo results based on series with at least one seasonal unit root show that spurious regressions are very likely if seasonal dummies are used to remove seasonality. Applications to ten real GDP series provide supporting evidence for the spurious regression phenomenon. However, seasonal dummies may provide a reasonable approximation in certain cases. An alternative approach is to use the seasonal filter S(L).