Are Seasonal Patterns Constant over Time? A Test for Seasonal Stability

Abstract

This paper introduces Lagrange multiplier tests of the null hypothesis of no unit roots at seasonal frequencies against the alternative of a unit root at either a single seasonal frequency or a set of seasonal frequencies. The tests complement those of D. Dickey, D. Hasza, and W. Fuller (1984) and S. Hylleberg, et al. (1990), which examine the null of seasonal unit roots. The authors derive an asymptotic distribution theory for the tests and investigate their size and power with a Monte Carlo exercise. Application of three sets of seasonal variables shows that, in most cases, seasonality is nonstationary.