Problem
Research questions and friction points this paper is trying to address.
irregular sampling
multivariate time series
Earth observation
astronomical measurements
discrete-time framework
Earth and space observations meet complex algebras: from complex to octonions for multivariate autoregressive time series analysis
🤖 AI Summary
论文提出了一种基于超复数自回归过程的框架，用于处理不规则时间间隔下的多变量时间序列分析问题，并通过卡尔曼滤波技术估计模型参数。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
hypercomplex autoregressive processes
irregular sampling
state-space system
Kalman filtering
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