This paper proposes an ADF coefficient test for detecting the presence of a unit root in ARMA models of unknown order. Our approach is fully parametric. When the time series has an unknown deterministic trend, we propose a modified version of the ADF coefficient test based on quasi-differencing...

Tests based on the quantile regression process can be formulated like the classical Kolmogorov-Smirnov and Cramer-von-Mises tests of goodness-of-fit employing the theory of Bessel processes as in Kiefer (1959). However, it is frequently desirable to formulate hypotheses involving unknown...

Several widely used tests for a changing mean exhibit nonmonotonic power in finite samples, due to "incorrect" estimation of nuisance parameters under the alternative. In this paper, we study the issue of nonmonotonic power in testing for changing mean. We investigate the asymptotic power...