The semiparametric asymmetric stochastic volatility model with time-varying parameters: The case of US inflation

•A semiparametric asymmetric stochastic volatility model with time-varying parameters is considered.•An efficient Markov Chain Monte Carlo estimation algorithm is developed.•The proposed model is applied to inflation modeling.•The proposed model shows positive correlation between inflation and volatility.•The proposed model forecasts better that competing models.

We propose a semiparametric extension of the time-varying parameter regression model with asymmetric stochastic volatility. For parameter estimation we use Bayesian methods. We illustrate our methods with an application to US inflation.