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.

翻译：引入了一种用于分析非正常间距所观测的时间序列的新颖的一阶移动平均模型。提出了两种定义,在高西度下是等效的。第一个定义依赖于通常分布的数据和第二阶时的规格。第二个定义更灵活,因为它允许考虑其他分布假设。统计属性与单步线性线性预测器及其平均平方差错一起进行调查。确定在一般情况下,该过程严格固定在正常状态下,一般情况下的固定状态较弱。讨论了最大可能性和靴套估计程序,并通过蒙特卡洛实验对这些估计数的有限抽样行为进行了评估。在这些模拟中,这两种方法在估计偏差和标准错误方面都表现良好,即使抽样大小较小。此外,我们还表明,对于非加西数据,对于图式和通用错误分布,模型的参数可以尽可能精确地估计。拟议的IMA模型与连续的自动递增平均模型(CARMA)相比,展示了良好的性能。最后,用两个模型展示了实际应用和拟议数据的实际效用。