Non-Markovian Regime Switching with Endogenous States and Time-Varying State Strengths

This article presents a non-Markovian regime switching model in which the regime states depend on the sign of an autoregressive latent variable. The magnitude of the latent variable indexes the `strength' of the state or how deeply the system is embedded in the current regime. The autoregressive nature of this non-Markovian regime switching implies time-varying state transition probabilities, even in the absence of an exogenous covariate. Furthermore, with time-varying regime strengths, the expected duration of a regime is time-varying. In this framework, it is natural to allow the autoregressive latent variable to be endogenous so that regimes are determined jointly with the observed data. We apply the model to GDP growth, as in Hamilton (1989), Albert and Chib (1993) and Filardo and Gordon (1998) to illustrate the relation of the regimes to NBER-dated recessions and the time-varying expected durations of regimes