APPROXIMATION TO THE LIMITING DISTRIBUTION OF t- AND F-STATISTICS IN TESTING FOR SEASONAL UNIT ROOTS
推导了季节性单位根检验中t和F统计量极限分布的矩生成函数，并证明其可用Gram-Charlier级数等分布良好近似，有助于改进检验的临界值计算。
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.