Testing for Seasonal Unit Roots by Frequency Domain Regression

Joanne Ercolani, Marcus Chambers, Robert Taylor

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


This paper develops univariate seasonal unit root tests based on spectral regression estimators. An advantage of the frequency domain approach is that it enables serial correlation to be treated non-parametrically. We demonstrate that our proposed statistics have pivotal limiting distributions under both the null and near seasonally integrated alternatives when we allow for weak dependence
in the driving shocks. This is in contrast to the popular seasonal unit root tests of, among others, Hylleberg et al. (1990) which treat serial correlation parametrically via lag augmentation of the test regression. Moreover, our analysis allows for (possibly innite order) moving average behaviour in the shocks, while extant large sample results pertaining to the Hylleberg et al. (1990) type tests are based on the assumption of a finite autoregression. The size and power properties of our proposed frequency domain regression-based tests are explored and compared for the case of quarterly data with those of the tests of Hylleberg et al. (1990) in simulation experiments.
Original languageEnglish
JournalJournal of Econometrics
Early online date5 Sept 2013
Publication statusPublished - 2013


  • Seasonal unit root tests
  • frequency domain regression
  • spectral density estimator


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