An Unobserved-Component Model With Switching Permanent and Transitory Innovations
提出一个由马尔可夫过程控制创新类型的不可观测成分模型，能同时描述数据的平稳与非平稳行为，并应用于美国季度实际GDP，发现超过80%样本期以单位根非平稳为主，且非平稳（平稳）期与NBER扩张（衰退）期高度吻合。
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.