On seasonal cycles, unit roots, and mean shifts

The interpretation of seasonality in terms of economic behavior depends on the form of the econometric time-series model that allows for a description of seasonality. Popular models often assume either approximate deterministic seasonality (cf. Miron (1996)) or stochastic trend seasonality (cf. Hylleberg (1994)). Inference from an inappropriate model can be shown to be invalid. Since much graphical evidence clearly suggests that seasonal fluctuations are not constant over time, we investigate whether the finding of seasonal unit roots can be due to neglected mean shifts. We provide relevant asymptotic theory and critical values for various test statistics. For a set of real gross domestic product series we find that much evidence for seasonal unit roots tends to disappear when a shift in the seasonal means is allowed. When we incorporate deterministic mean shifts in the deterministic seasonality model, we find that qualitative results on the presence of the so-called seasonal cycle documented in, for example, Miron and Beaulieu (1996) are robust.