An irregularly spaced first-order moving average model

Abstract

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.