For many studies in which data are collected sequentially in time, the sensitivity of the measurement is limited and an exact value can be recorded only if it falls within a specified range. This gives rise to a censored time series. In this article, we present a methodology for regression analysis of censored time series data. We fit autoregressive models to account for the time dependence. Two numerical methods for full likelihood estimation and an approximate method are discussed. The methods are illustrated with air pollution data subject to lower limits of detection.