Abstract
This article proposes an unobserved-component model in which component innovations are governed by a state variable that follows a Markov process. The proposed model is capable of describing both stationary and nonstationary behaviors of real data and allows the random innovations to have permanent and transitory effects in different periods. The model also permits a deterministic trend with or without breaks and hence bridges the gap between the trend-stationary model and a random walk with drift. For ease in presentation and in application, our discussion focuses on the model consisting of a random-walk component and a stationary autoregressive moving average component. However, the proposed model is much more flexible. We investigate properties of the proposed model and derive an estimation algorithm. We also propose a simulation-based test to distinguish between the proposed model and an autoregressive integrated moving average model. For application, we apply the model to U.S. quarterly real gross domestic product and find that unit-root nonstationarity is likely to be the prevailing dynamic pattern in more than 80% of the sample periods. Because nonstationarity (stationarity) periods match the National Bureau of Economic Research dating of expansions (recessions) closely, our result suggests that the innovations in expansion (recession) are more likely to have a permanent (transitory) effect. © 2005 American Statistical Association.