REGRESSION-BASED SEASONAL UNIT ROOT TESTS
提出了季节性单位根假设的子假设特征定理，并构建了允许一般季节性特征的回归检验，给出了极限分布理论，发现复杂频率的t统计量渐近分布会改变，而零频率和奈奎斯特频率的t统计量及复杂频率的F统计量不受影响。
The contribution of this paper is threefold. First, a characterization theorem of the subhypotheses comprising the seasonal unit root hypothesis is presented that provides a precise formulation of the alternative hypotheses associated with regression- based seasonal unit root tests. Second, it proposes regression-based tests for the seasonal unit root hypothesis that allow a general seasonal aspect for the data and are similar both exactly and asymptotically with respect to initial values and seasonal drift parameters. Third, limiting distribution theory is given for these statistics where, in contrast to previous papers in the literature, in doing so it is not assumed that unit roots hold at all of the zero and seasonal frequencies. This is shown to alter the large-sample null distribution theory for regression t -statistics for unit roots at the complex frequencies, but interestingly to not affect the limiting null distributions of the regression t -statistics for unit roots at the zero and Nyquist frequencies and regression F -statistics for unit roots at the complex frequencies. Our results therefore have important implications for how tests of the seasonal unit root hypothesis should be conducted in practice. Associated simulation evidence on the size and power properties of the statistics presented in this paper is given that is consonant with the predictions from the large-sample theory.