Hylleberg, Engle, Granger, and Yoo (1990, Journal
of Econometrics 44, 215–238), Beaulieu and Miron
(1993, Journal of Econometrics 55, 305–328),
Ghysels, Lee, and Noh (1994, Journal of Econometrics
62, 415–442), Smith and Taylor (1998, Journal
of Econometrics 85, 269–288; 1999, Journal
of Time Series Analysis 20, 453–476; 1999, Discussion
paper 99-15 in economics, University of Birmingham), and
Taylor (1998, Journal of Time Series Analysis
19, 349–368) have developed a method of testing for
seasonal unit roots of zero and nonzero frequencies. They
propose to use t- and F-statistics as
criteria that are obtained from an auxiliary regression
and find their limiting distributions as the number of
observations becomes large. Their limiting distributions
are expressed by means of Brownian motions. In this paper
the moment generating functions associated with the limiting
distributions are derived, and it is shown, as in Nabeya
(2000, Econometric Theory 16, 200–230),
that the limiting distribution of t is well approximated
by a distribution given in Gram–Charlier series.
The limiting distribution of F is also well approximated
by another type of distribution.
Testing for Seasonal Unit Roots in Monthly Panels of Time Series*
