  A novel first-order autoregressive moving average model for analyzing
discrete-time series observed at irregularly spaced times is introduced. Under
Gaussianity, it is established that the model is strictly stationary and
ergodic. In the general case, it is shown that the model is weakly stationary.
The lowest dimension of the state-space representation is given along with the
one-step linear predictors and their mean squared errors. The maximum
likelihood estimation procedure is discussed, and their finite-sample behavior
is assessed through Monte Carlo experiments. These experiments show that bias,
root mean squared error, and coefficient of variation are smaller when the
length of the series increases. Further, the method provides good estimations
for the standard errors, even with relatively small sample sizes. Also, the
irregularly spaced times seem to increase the estimation variability. The
application of the proposed model is made through two real-life examples. The
first is concerned with medical data, whereas the second describes an
astronomical data set analysis.
