This paper proposes a class of procedures that consistently classify the stochastic component of a time series as being integrated either of order zero (l(0» or one (l(1» for general 1(0) and 1(1) processes. These procedures entail the evaluation of the asymptotic likelihoods of certain statistics under the 1(0)and 1(1) hypotheses. These likelihoods do not depend on nuisance parameters describing short-run dynamics and diverge asymptotically, so their ratio provides a consistent basis for classifying a process as 1(1) or 1(0). Bayesian inference can be performed by placing prior mass only on the point hypotheses "1(0)" and "1(1)" without needing to specify parametric priors within the classes of 1(0) and 1(1) processes; the result is posterior odds ratios for the 1(0) and 1(1) hypotheses. These procedures are developed for general polynomial and piecewise linear detrending. When applied to the Nelson-Plosser data with linear detrending, they largely support the original Nelson-Plosser inferences. With piecewise-linear detrending these data are typically uninformative, producing Bayes factors that are close to one.
