A Seasonal Unit-Root Test with Stata

Abstract

Many economic time series exhibit important systematic fluctuations within the year, i.e., seasonality. In contrast to usual practice, I argue that using original data should always be considered, although the process is more complicated than that of using seasonally adjusted data. Motivations to use unadjusted data come from the information contained in their peaks and troughs and from economic theory. One major complication is the possible unit root at seasonal frequencies. In this article, I tackle the issue of implementing a test to identify the source of seasonality. In particular, I follow Hylleberg et al. (1990, Journal of Econometrics 44: 215–238) for quarterly data.