ASYMPTOTIC DISTRIBUTIONS FOR REGRESSION-BASED SEASONAL UNIT ROOT TEST STATISTICS IN A NEAR-INTEGRATED MODEL

Paulo Rodrigues and Robert Taylor

Econometric Theory, 2004, vol. 20, issue 4, 645-670

Abstract: In this paper we derive representations for the limiting distributions of the regression-based seasonal unit root test statistics of Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238) and Beaulieu and Miron (1993, Journal of Econometrics 55, 305–328), inter alia, when the underlying process displays near seasonal integration. Our results generalize those presented in previous studies by allowing for an arbitrary seasonal periodicity (including the nonseasonal case), a wide range of possible assumptions on the initial conditions, a range of (seasonal) deterministic mean effects, and finite autoregressive behavior in the driving shocks. We use these representations to simulate the asymptotic local power functions of the seasonal unit root tests, demonstrating a significant dependence on serial correlation nuisance parameters in the case of the pairs of t-statistics, but not the associated F-statistic, for unit roots at the seasonal harmonic frequencies. Monte Carlo simulation results are presented that suggest that the local limiting distribution theory provides a good approximation to the finite-sample behavior of the statistics. Our results lend further weight to the advice of previous authors that inference on the unit root hypothesis at the seasonal harmonic frequencies should be based on the F-statistic, rather than on the associated pairs of t-ratios.We are grateful to Bruce Hansen and two anonymous referees for their helpful comments and suggestions on earlier versions of this paper.

Date: 2004
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