Unit Roots, Change, and Decision Bounds

The problem of optimal decision between unit roots, trend stationarity and trend stationarity with structural breaks is considered. Each of three classes is represented by a hierarchically random process whose parameters are distributed in a non-informative way based on a simple rule. Given a well-accepted parameterization, parameters are distributed uniformly if they are bounded by admissibility conditions, and standard normally if they are unbounded. The prior frequency for all three processes is the same. Classification of observed trajectories into any of the three classes is based on two information condenser statistics *1 and *2. *1 is the traditional Dickey-Fuller t-test statistic that allows for a linear trend. *2 is a heuristic statistic that condenses information on structural breaks. Two loss functions are considered for determining decision bounds within the ( *1, *2) space. Firstly, quadratic discrete loss expresses the interest of a researcher attempting to find out the true model. Secondly, prediction error loss expresses the interest of a forecaster who sees models as intermediate aims. For both loss functions and the empirically relevant sample sizes of T = 50, 100, 150, 200, optimal decision contours are established by means of Monte Carlo simulation.