A time-varying threshold STAR model with applications

Smooth-transition autoregressive (STAR) models, competitors of Markov-switching models, are limited by an assumed time-invariant threshold level. We augment the STAR model with a time-varying threshold that can be interpreted as a 'tipping level' where the mean and dynamics of the VAR shift. Thus, the time-varying latent threshold level serves as a demarcation between regimes. We show how to estimate the model in a Bayesian framework using a Metropolis step and an unscented Kalman filter proposal. To show how allowing time variation in the threshold can affect the results, we present two applications: a model of the natural rate of unemployment and a model of regime-dependent government spending.