Gaussian tests for seasonal unit roots based on Cauchy estimation and recursive mean adjustments

We propose tests for seasonal unit roots whose limiting null distributions are always standard normal regardless of the period of seasonality and type s of mean adjustments. The seasonal models of Dickey, Hasza and Fuller (198 4. Journal of American Statistical Association 79, 355-367) (DHF) and Hylle berg, Engle, Granger and Yoo (1990. Journal of Econometrics 44, 215-238) (H EGY) are considered. For estimating parameters related to the seasonal unit roots, regressor signs are used as instrumental variables while recursive sample means are used for adjusting the seasonal means. In addition to norm ality of the limiting null distributions, in seasonal mean models, the recu rsive mean adjustment provides the new tests with locally higher powers tha n those of the existing tests of DHF and HEGY based on the ordinary least-s quares estimators. If data have a strong linear time trend, the recursive m ean adjustment is a source of both power gains of some tests for local alte rnatives and power losses of all tests for other alternatives. Limiting nor mality allow evaluation of p-values and testing joint significance of subse ts of seasonal unit roots. (C) 2000 Elsevier Science S.A. All rights reserv ed. JEL classification: C12; C22.