Nearly Efficient Likelihood Ratio Tests for Seasonal Unit Roots

In an important generalization of zero frequency autoregressive unit root tests, Hylleberg, Engle, Granger & 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 & Stock (1996), i.e. that 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 & Taylor (2007). However, both require the choice of a GLS detrending parameter, which our likelihood ratio tests do not