On the Properties of Regression-Based Seasonal Unit Root Tests in the Presence of Higher Order Serial Correlation

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Colleges, School and Institutes


We analyze the behavior of widely used regression-based tests for seasonal unit roots when the shocks are serially correlated. We show, in the quarterly case, that the common assumption that serial correlation may be accommodated by augmenting the test regression with appropriate lagged seasonal differences is only partially correct. The limiting null distributions of t statistics for unit roots at the zero and Nyquist frequencies aw corrected by the lag augmentation, but those of t statistics at the harmonic seasonal frequency are nor. Fortunately. the joint F-type tests at the harmonic frequency, which are in widespread use, do remain pivotal and should therefore supplant the individual t statistics in applied work. That the latter are indeed badly behaved in finite samples, while the F-type tests are correctly sized, is demonstrated by a Monte Carlo experiment.


Original languageEnglish
Pages (from-to)374-379
Number of pages6
JournalJournal of Business and Economic Statistics
Publication statusPublished - 1 Jul 2001


  • serially correlated shocks, seasonal unit-root tests