A NOTE ON TESTING FOR UNIT ROOTS IN THE UNOBSERVABLE TREND COMPONENT OF A STRUCTURAL MODEL

Testing for unit roots is a common practice in observable stochastic processes and there is abundant literature on this topic. However, sometimes, one is faced with the same problem but in the case where the processes of interest are latent or unobservable. In this paper, empirical distributions of the usual unit-root test statistics are obtained for the trend component of some particular structural models, which are based on optimal predictions (as the observed data) of the trend stochastic process. It is found that these statistical tests tend to be most powerful than the usual Dickey-Fuller tests.