The problem of estimating the output in missing-data situations is addressed, in case a process model is present. A simple algorithm is presented that uses the input-output model(difference equation), replacing the unknown past values by estimates when necessary. It is compared to state-space approaches such as time-varying Kalman filtering. The analysis of its convergence is carried out for the particular case of dual-rate scarce sampling patterns. The effects of disturbances are also studied. The use of extended order models allows the design of the desired error dynamics. Applications such as parameter estimation and the control under scarce data operation are outlined.