Abstract This article considers the estimation of dynamic Tobit models and Tobit models with ARCH or GARCH disturbances in the time series context. Due to censoring, some disturbances cannot be observed. The simulated maximum likelihood method is feasible for the estimation of such models. A general simulation method that has broad applicability is provided. Variance reduction in simulation is possible for important models that have a renewal property. For long time series, the numerical underflow issue can be overcome with a numerically stable formation of simulated likelihood. Monte Carlo results are provided for dynamic models and models with ARCH and GARCH disturbances.