Testing for Unit Roots in Seasonal Time Series

Abstract

Part of the increasing interest in the treatment of seasonality in economic 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 theoretically and via simulation the properties of Dickey-Fuller-type tests in seasonal time series which have roots at frequencies other than the zero frequency. We also investigate the properties of the standard testing procedures for unit roots in seasonal time series via Monte Carlo simulations. 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 appropriate autoregressive correction terms are augmented to the model. Our Monte Carlo simulations reveal that tests for unit roots at seasonal frequencies have severe size distortions in many cases commonly encountered in practice. While we find the procedure proposed by Hylleberg, Engle, Granger, and Yoo (1990) the most useful among the alternative procedures, we caution users of many remaining serious obstacles when testing for unit roots in seasonal time series.