Modeling Seasonal Unit Roots as a Simple Empirical Method to Handle Autocorrelation in Demand Systems: Evidence from UK Expenditure Data

Economic data with substantial seasonality are likely to have unit roots in more than one frequency. Using non-alcoholic beverage expenditure data from the United Kingdom, we empirically show that the absence of unit roots in one frequency (e.g. monthly) does not imply the absence of unit roots in some other frequencies (e.g. quarterly, bi-annually, and annually). Given the evidence of seasonal unit roots, we estimated one static and three dynamic quadratic almost ideal demand system (QUAIDS) specifications. We found that the seasonal-habit QUAIDS outperforms the static, myopic-habit and rational-habit specifications. Additionally, we show that taking into account seasonal habits helps correct autocorrelation in residuals. Simply put, given the presence of seasonal unit roots, lagged seasonal terms can be a useful simple tool for practitioners modeling expenditure data using demand systems.