  Time series observations are ubiquitous in astronomy, and are generated to
distinguish between different types of supernovae, to detect and characterize
extrasolar planets and to classify variable stars. These time series are
usually modeled 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 dependency 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.
