On the Properties of Regression-Based Tests for Seasonal Unit Roots in the Presence of Higher-Order Serial Correlation
分析序列相关对季节性单位根回归检验的影响，发现季度数据中滞后调整仅修正部分频率的t统计量，而谐波频率的F检验稳健，蒙特卡洛实验证实其有限样本表现更优。
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.