The finite sample distribution of the KPSS test

This paper gives numerical approximations of the finite sample distribution of the KPSS test statistic. We use two types of approximations depending on whether we estimate the long-run variance or not. In the known variance case we apply a very simple Laplace inversion formula, while in the unknown case we use saddlepoint approximation to calculate the right-hand tail of the distribution of the KPSS test statistic. In the unknown variance case, we also investigate the robustness of the test to non i.i.d. innovations.