The paper presents general local level model with stochastic volatility, recently proposed for U.S. inflation by Stock and Watson. The main purpose is to present and compare other local level model specifications, especially with Normal GARCH and Student-t GARCH disturbances. The paper is a full Bayesian analysis and concerns inflation in Poland during 1992-2007. The model selection and posterior estimates provide strong evidence in favor of a model with heavy-tailed disturbances in the core component, and the transitory component. Also, after the system transformations in the early 90's, the volatility of the disturbances driving both components have been substantially decreasing over time.