ASYMPTOTIC DISTRIBUTIONS FOR REGRESSION-BASED SEASONAL UNIT ROOT TEST STATISTICS IN A NEAR-INTEGRATED MODEL
推导了当数据接近季节性单位根时，几种常用季节性单位根检验统计量的极限分布，并模拟了局部渐近功效，发现谐波频率处应使用F统计量而非t统计量。
In this paper we derive representations for the limiting distributions of the regression-based seasonal unit root test statistics of Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238) and Beaulieu and Miron (1993, Journal of Econometrics 55, 305–328), inter alia, when the underlying process displays near seasonal integration. Our results generalize those presented in previous studies by allowing for an arbitrary seasonal periodicity (including the nonseasonal case), a wide range of possible assumptions on the initial conditions, a range of (seasonal) deterministic mean effects, and finite autoregressive behavior in the driving shocks. We use these representations to simulate the asymptotic local power functions of the seasonal unit root tests, demonstrating a significant dependence on serial correlation nuisance parameters in the case of the pairs of t-statistics, but not the associated F-statistic, for unit roots at the seasonal harmonic frequencies. Monte Carlo simulation results are presented that suggest that the local limiting distribution theory provides a good approximation to the finite-sample behavior of the statistics. Our results lend further weight to the advice of previous authors that inference on the unit root hypothesis at the seasonal harmonic frequencies should be based on the F-statistic, rather than on the associated pairs of t-ratios.We are grateful to Bruce Hansen and two anonymous referees for their helpful comments and suggestions on earlier versions of this paper.