TESTING FOR SEASONAL UNIT ROOTS IN PERIODIC INTEGRATED AUTOREGRESSIVE PROCESSES

摘要

This paper examines the implications of applying the Hylleberg,Engle,Granger,and Yoo(1990,Journal of Econometrics 44,215-238)(HEGY)seasonal root tests to a process that is periodically integrated.As an important special case,the random walk process is also considered,where the zero-frequency unit root t-statistic is shown to.converge to the Dickey-Fuller distribution and all seasonal unit root statistics diverge.For periodically integrated processes and a sufficiently high order of augmentation,the HEGY t-statistics for unit roots at the zero and semiannual frequencies both converge to the same Dickey-Fuller distribution.Further,the HEGY joint test statistic for a unit root at the annual frequency and all joint test statistics across frequencies converge to the square of this distribution.Results are also derived for a fixed order of augmentation.Finite-sample Monte Carlo results indicate that,in practice,the zero-frequency HEGY statistic(with augmentation)captures the single unit root of the periodic integrated process,but there may be a high probability of incorrectly concluding that the process is seasonally integrated.