论文标题
一种新型的一阶自回旋运动平均模型，以分析离散时间串联不规则观察到
A Novel First-Order Autoregressive Moving Average Model to Analyze Discrete-Time Series Irregularly Observed
论文作者
论文摘要
引入了一个新型的一阶自回旋运动平均模型，用于分析在不规则间隔时间观察到的离散时间串联的新型自动运动平均模型。在高斯性下，可以确定该模型是严格的静止和奇异的。在一般情况下，这表明该模型是弱静止的。状态空间表示的最低维度与一步线性预测指标及其平方误差一起给出。讨论了最大似然估计程序，并通过蒙特卡洛实验评估其有限样本行为。这些实验表明，当系列的长度增加时，偏差，均值平方误差和变异系数较小。此外，该方法为标准误差提供了良好的估计，即使样本量相对较小。而且，不规则间隔的时间似乎增加了估计变异性。提出的模型的应用是通过两个现实生活中的示例进行的。第一个与医学数据有关，而第二个描述了天文数据集分析。
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.
