ARE SEASONAL PATTERNS CONSTANT OVER TIME - A TEST FOR SEASONAL STABILITY

This article 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 Dickey, Hasza, and Fuller and Hylleberg, Engle, Granger, and Yoo that examine the null of seasonal unit roots. We derive an asymptotic distribution theory for the tests, and investigate their size and power with a Monte Carlo exercise. Application of the tests to three sets of seasonal variables shows that in most cases seasonality is nonstationary.