Time series observations are ubiquitous in astronomy and are generated, for example, to distinguish between different types of supernovae to detect and characterize extrasolar planets and to classify variable stars. These time series are usually modelled using a parametric and/or physical model that assumes independent and homoscedastic errors, but in many cases, these assumptions are not accurate and there remains a temporal dependence structure on the errors. This can occur, for example, when the proposed model cannot explain all the variability of the data or when the parameters of the model are not properly estimated. In this work, we define an autoregressive model for irregular discrete-time series based on the discrete time representation of the continuous autoregressive model of order 1. We show that the model is ergodic and stationary. We further propose a maximum likelihood estimation procedure and assess the finite sample performance by Monte Carlo simulations. We implement the model on real and simulated data from Gaussian as well as other distributions, showing that the model can flexibly adapt to different data distributions. We apply the irregular autoregressive model to the residuals of a transit of an extrasolar planet to illustrate errors that remain with temporal structure. We also apply this model to residuals of an harmonic fit of light curves from variable stars to illustrate how the model can be used to detect incorrect parameter estimation.
