Distribution approximation of unit root tests in autoregressive models

The present work applies saddlepoint approximation to calculate the left-hand tail of the distribution of the unit root t test and an asymptotic equivalent test under the null hypothesis of a unit root. (This is the tail of interest when testing against a stationary alternative.) The saddlepoint equation is solved numerically. Distribution approximations are obtained both in the asymptotic and finite-sample cases. In the finite-sample case, two slightly different methods are suggested and compared.