A component-driven model for regime switching and its empirical evidence

In this paper we propose a general component-driven model to analyze economic data with different characteristics (or regimes) in different time periods. Motivated by empirical data characteristics, our discussion focuses on a simple model driven by a random walk component and a stationary ARMA component that are governed by a Markovian state variable. The proposed model is capable of describing both stationary and non-stationary behaviors of data and allows its random innovations to have both permanent and transitory effects. This model also permits a deterministic trend with or without breaks and hence constitutes intermediate cases between the trend-stationary model and a random walk with drift. We investigate properties of the proposed model and derive an estimation algorithm. A simulation-based test is also proposed to distinguish between the proposed model and an ARIMA model. In empirical application, we apply this model to U.S.\ quarterly real GDP and find that unit-root nonstationarity is likely to be the prevailing dynamic pattern in more than 80 percent of the sample periods. Our result suggests that the innovations in expansions (recessions) are more likely to have a permanent (transitory) effect.