Abstract :
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+ Finitesample
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+
