许多数据集表现为在不规则时间间隔上观测的多变量时间序列，尤其在地球观测和天文测量中。经典时间序列模型假设时间是离散的且观测发生在等间距的时间点，这限制了其在观测间隔变化时捕捉动态的能力。现有的不规则采样方法依赖于连续时间公式，并假设观测间隔足够小。我们通过引入一个离散时间框架来解决这一局限性，该框架能够适应不规则的观测间隔，同时保留多变量依赖结构。我们提出了一个基于超复数自回归过程的不规则观测多变量时间序列分析框架。该框架将多变量观测嵌入超复数代数结构中，使得多个变量及其相互作用可以在单个数学实体中表示，同时纳入不规则的观测间隔。由此产生的过程具有结构化矩阵表示，使模型能够表达为状态空间系统。这种公式提供了一种估计方法，其中可以使用卡尔曼滤波技术推断模型参数。状态空间表示允许在存在不规则采样间隔的情况下进行递归估计和预测。该方法论的性能通过遥感及天文数据集的应用得到验证，这些数据集的观测发生在非均匀时间间隔上。结果表明，该方法能够捕捉传统时间序列技术难以建模的动态特征和跨变量相互作用。所提出的框架为分析不...

Many datasets arise as multivariate time series observed at irregular time intervals, particularly in Earth observation and astronomical measurements. Classical time-series models assume that time is discrete and observations occur at equally spaced intervals, limiting their ability to capture dynamics when observation gaps vary. Existing approaches to irregular sampling rely on continuous-time formulations, which assume that observation intervals are sufficiently small. We address this limitation by introducing a discrete-time framework that accommodates irregular observation gaps while preserving multivariate dependence structures. We introduce a framework for the analysis of irregularly observed multivariate time series based on hypercomplex autoregressive processes. The framework embeds multivariate observations into a hypercomplex algebraic structure, allowing multiple variables and their interactions to be represented within a single mathematical entity while incorporating irregular observation gaps. The resulting process admits a structured matrix representation, which enables the model to be expressed as a state-space system. This formulation provides an estimation methodology in which model parameters can be inferred using Kalman filtering techniques. The state-space representation allows recursive estimation and prediction in the presence of irregular sampling intervals. The performance of the methodology is illustrated through data and applications to remote sensing and astronomical datasets, where observations occur at nonuniform time intervals. The results demonstrate that the approach captures dynamics and cross-variable interactions difficult to model using traditional time-series techniques. The proposed framework provides a methodology for analyzing irregularly sampled multivariate time series and opens possibilities for modeling observational data across disciplines.