Saddlepoint Approximations for Optimal Unit Root Tests

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 proven to yield valid asymptotic inference. Numerical evidence demonstrates superiority over approximations for a directly comparable test based on simulation of its limiting stochastic representation. In addition, because the saddlepoint offers an explicit representation P-value sensitivity to model specification is easily analyzed, here in the context of the Nelson and Plosser data.