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

Seiji Nabeya

12 citations0/0 files storedEconometric Theory

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Monetary Policy and Economic Impact Time Series Analysis and Forecasting Diverse Scientific and Economic Studies

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.

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1979Distribution of the Estimators for Autoregressive Time Series with a Unit Root 1984Testing for Unit Roots in Seasonal Time Series 1993Seasonal unit roots in aggregate U.S. data 1998Additional critical values and asymptotic representations for seasonal unit root tests 1999Likelihood Ratio Tests for Seasonal Unit Roots 1998Testing for Unit Roots in Monthly Time Series 1999ASYMPTOTIC MOMENTS OF SOME UNIT ROOT TEST STATISTICS IN THE NULL CASE

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