Score-driven models provide a solution to the problem of modelling time series when the observations are subject to censoring and location and/or scale may change over time. The method applies to generalized-t and EGB2 distributions, as well as to the normal distribution. A set of Monte Carlo experiments show that the score-driven model provides good forecasts even when the true model is parameterdriven. The viability of the new models is illustrated by fitting them to data on Chinese stock returns.