This paper considers the problems of parameter identification and output estimation with possibly irregularly missing output data, using output error models. By means of an auxiliary model (or reference model) approach, we present a recursive least-squares algorithm to estimate the parameters of missing data systems, and establish convergence properties for the parameter and missing output estimation in the stochastic framework. The basic idea is to replace the unmeasurable inner variables with the output of an auxiliary model. Finally, we test the effectiveness of the algorithm with an example system. Copyright © 2009 John Wiley & Sons, Ltd.