The problem of optimal decision among unit roots, trend stationarity, and trend stationarity with structural breaks is considered. Each class is represented by a hierarchically random process whose parameters are distributed in a non-informative way. The prior frequency for all three processes is the same. Observed trajectories are classified by two information condenser statistics zeta1 and zeta2. zeta1 is the traditional Dickey-Fuller t-test statistic that allows for a linear trend. zeta2 is a heuristic statistic that condenses information on structural breaks. Two loss functions are considered for determining decision contours within the (zeta1, zeta2) space. Whereas quadratic discrete loss expresses the interest of a researcher attempting to find out the true model, 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.
time series integrated processes structural breaks loss function