Unit roots, change, and decision bounds - Robert M. Kunst (Institute for Advanced Studies (IHS), 1998)
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.
Keywords: C22; C44; 330; time series; integrated processes; structural breaks; loss; function