APPROXIMATION TO THE LIMITING DISTRIBUTION OF t- AND F-STATISTICS IN TESTING FOR SEASONAL UNIT ROOTS

Seiji Nabeya

Econometric Theory, 2001, vol. 17, issue 04, pages 711-737

Abstract: 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.

Date: 2001

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