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. In this model, regimes have dynamics, not only persistence, so that one regime can gradually give way to another. 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. The article makes use of the Metropolis-Hastings algorithm to make multi-move draws of the latent regime strength variable, where the extended Kalman filter provides a valid proposal density for the latent variable