TESTING FOR UNIT ROOTS IN SEASONAL TIME-SERIES - SOME THEORETICAL EXTENSIONS AND A MONTE-CARLO INVESTIGATION

Part of the increasing interest in the treatment of seasonality in eco nomic time series has focused on detecting the presence of unit roots at some of the seasonal frequencies as well as at the zero frequency. In this paper we introduce new test statistics, analyze both theoretic ally and via simulation the properties of Dickey-Fuller-type tests in seasonal time series which have roots at frequencies other than the ze ro frequency. We also investigate the properties of the standard testi ng procedures for unit roots in seasonal time series via Monte Carlo s imulations. We show that the Dickey-Fuller tests can still be used to test for a unit root at the zero frequency to the extent that appropri ate autoregressive correction terms are augmented to the model. Our Mo nte Carlo simulations reveal that tests for unit roots at seasonal fre quencies have severe size distortions in many cases commonly encounter ed in practice. While we find the procedure proposed by Hylleberg, Eng le, Granger, and Yoo (1990) the most useful among the alternative proc edures, we caution users of many remaining serious obstacles when test ing for unit roots in seasonal time series.