© 1988 by Biometrika Trust
Testing for a unit root in time series regression
Cowles Foundation for Research in Economics, Yale University Yale Station, New Haven, Connecticut 06520, U.S.A.
Département des Sciences Economiques, Université de Montreal Montréal, Québec, Canada H3C 3J7
This paper proposes new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly heterogeneously distributed data. The tests accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend. The limiting distributions of the statistics are obtained under both the unit root null and a sequence of local alternatives. The latter noncentral distribution theory yields local asymptotic power functions for the tests and facilitates comparisons with alternative procedures due to Dickey & Fuller. Simulations are reported on the performance of the new tests in finite samples.
Key Words: Brownian motion • Noncentral distribution • Time series • Unit root • Weak convergence
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