SADDLEPOINT AND ESTIMATED SADDLEPOINT APPROXIMATIONS FOR OPTIMAL UNIT ROOT TESTS
为最优单位根检验的分布提供了鞍点尾部概率近似，在严格假设下给出误差阶数，并在更一般的鞅差线性过程中证明估计鞍点能实现有效渐近推断，数值证据显示其有限样本表现优于基于模拟的近似。
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.