Semiparametric Bayesian inference for time-varying parameter regression models with stochastic volatility

•A semiparametric stochastic volatility model with time-varying parameters is considered.•An efficient Markov Chain Monte Carlo estimation algorithm is proposed.•The proposed model is applied to inflation modelling.•The proposed model performs better than alternative specifications.

We develop a Bayesian semiparametric method to estimate a time-varying parameter regression model with stochastic volatility, where both the error distributions of the observations and parameter-driven dynamics are unspecified. We illustrate our methodology with an application to inflation.