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Published online by Cambridge University Press:  25 March 2011

Patrick Marsh*
University of York
*Address correspondence to Patrick Marsh, Department of Economics, University of York, YO105DD, United Kingdom; e-mail:


This paper provides a (saddlepoint) tail probability approximation for the distribution of an optimal unit root test. Under restrictive assumptions, Gaussianity, and known covariance structure, the order of error of the approximation is given. More generally, when innovations are a linear process in martingale differences, the estimated saddlepoint is proved to yield valid asymptotic inference. Numerical evidence, considered over a range of models, demonstrates some finite-sample superiority over approximations for a directly comparable test based on simulation of its limiting stochastic representation.

Copyright © Cambridge University Press 2011

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