This paper discusses an autoregressive model for the analysis of irregularly observed time series. The properties of this model are studied and a maximum likelihood estimation procedure is proposed. The finite sample performance of this estimator is assessed by Monte Carlo simulations, showing accurate estimators. We implement this model to the residuals after fitting an harmonic model to light-curves from periodic variable stars from the Optical Gravitational Lensing Experiment (OGLE) and Hipparcos surveys, showing that the model can identify time dependency structure that remains in the residuals when, for example, the period of the light-curves was not properly estimated.