Testing for Unit Roots in Monthly Time Series

Abstract

This paper is concerned with tests for seasonal roots in monthly univariate time series processes. The paper extends the procedures and tables of critical values due to Beaulieu and Miron (Seasonal unit roots in aggregate U.S. data. J. Economet. 55 (1993), 305–28) to obtain tests which are similar ( exactly and a symptotically) with respect to both the initial values of the process and the possibility of seasonal drifts under the seasonal unit root null hypothesis. We also develop test statistics which test simultaneously for a unit root at each frequency and for a unit root at each of the seasonal frequencies. Representations are derived for the limiting distributions of each of the test statistics proposed in this paper. We illustrate the practical usefulness of the proposed test statistics by a series of empirical applications

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