Tests of linear and logarithmic transformations for integrated processes

This article proposes nonnested tests of linear and logarithmic transformat ions of integrated processes against each other, where the innovations of b oth series follow autoregressive processes. It is shown that the null distr ibutions of the test statistics for both the linear and logarithmic transfo rmations are nonstandard when the processes have no drift, whereas they are asymptotically normal when the processes have positive drift. Monte Carlo experiments and illustrative empirical examples are provided to show the pr actical usefulness of the tests in differentiating between linear and logar ithmic transformations of a process in finite samples.