  A novel first-order moving-average model for analyzing time series observed
at irregularly spaced intervals is introduced. Two definitions are presented,
which are equivalent under Gaussianity. The first one relies on normally
distributed data and the specification of second-order moments. The second
definition provided is more flexible in the sense that it allows for
considering other distributional assumptions. The statistical properties are
investigated along with the one-step linear predictors and their mean squared
errors. It is established that the process is strictly stationary under
normality and weakly stationary in the general case. Maximum likelihood and
bootstrap estimation procedures are discussed and the finite-sample behavior of
these estimates is assessed through Monte Carlo experiments. In these
simulations, both methods perform well in terms of estimation bias and standard
errors, even with relatively small sample sizes. Moreover, we show that for
non-Gaussian data, for t-Student and Generalized errors distributions, the
parameters of the model can be estimated precisely by maximum likelihood. The
proposed IMA model is compared to the continuous autoregressive moving average
(CARMA) models, exhibiting good performance. Finally, the practical application
and usefulness of the proposed model are illustrated with two real-life data
examples.
