A Regime Shift Model with Nonparametric Switching Mechanism

In this paper, we propose a new class of regime shift models with flexible switching mechanism that relies on a nonparametric probability function of the observed threshold variables. The proposed models generally embrace traditional threshold models with contaminated threshold variables or heterogeneous threshold values, thus gaining more power in handling complicated data structure. We solve the identification issue by imposing either global shape restriction or boundary condition on the nonparametric probability function. We utilize the natural connection between penalized splines and hierarchical Bayes to conduct smoothing. By adopting different priors, our procedure could work well for estimations of smooth curve as well as discontinuous curves with occasionally structural breaks. Bayesian tests for the existence of threshold effects are also conducted based on the posterior samples from Markov chain Monte Carlo (MCMC) methods. Both simulation studies and an empirical application in predicting the U.S. stock market returns demonstrate the validity of our methods.