Nearly Efficient Likelihood Ratio Tests for Seasonal Unit Roots

Michael Jansson 1  and Morten Ørregaard Nielsen 2
  • 1 University of California, Berkeley and CREATES
  • 2 Queen’s University and CREATES

In an important generalization of zero frequency autoregressive unit root tests, Hylleberg, Engle, Granger, and Yoo (1990) developed regression-based tests for unit roots at the seasonal frequencies in quarterly time series. We develop likelihood ratio tests for seasonal unit roots and show that these tests are “nearly efficient” in the sense of Elliott, Rothenberg, and Stock (1996), i.e. their asymptotic local power functions are indistinguishable from the Gaussian power envelope. Nearly efficient testing procedures for seasonal unit roots have been developed, including point optimal tests based on the Neyman-Pearson Lemma as well as regression-based tests, e.g. Rodrigues and Taylor (2007). However, both require the choice of a GLS detrending parameter, which our likelihood ratio tests do not.

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The Journal of Time Series Econometrics (JTSE) serves as an internationally recognized outlet for important new research in both theoretical and applied classical and Bayesian time series, spatial and panel data econometrics. The scope of the journal includes papers dealing with estimation, testing and other methodological aspects involved in the application of time series and spatial analytic techniques to economic, financial and related data.