An infinite hidden Markov model with stochastic volatility

Abstract

This paper extends the Bayesian semiparametric stochastic volatility (SV-DPM) model. Instead of using a Dirichlet process mixture (DPM) to model return innovations, we use an infinite hidden Markov model (IHMM). This allows for time variation in the return density beyond that attributed to parametric latent volatility. The new model nests several special cases as well as the SV-DPM. We also discuss posterior and predictive density simulation methods for the model. Applied to equity returns, foreign exchange rates, oil price growth and industrial production growth, the new model improves density forecasts, compared with the SV-DPM, a stochastic volatility with Student's $t$ innovations and other fat-tailed volatility models.