AI 中文总结
本文从贝叶斯视角，基于功能时间序列的状态空间表示，提出新颖方法与分块吉布斯采样算法，在金融、温度数据集上验证了其检测功能时间序列结构畸变的有效性。
AI 中文摘要
在现代数据科学时代，高维数据集与功能数据集的快速增长，促使人们对范式转变与结构突变的研究兴趣日益浓厚。与经典的单变量时间序列不同，功能数据中的结构变化无需在整个定义域内同时发生，而是可能局部出现，在底层功能结构上产生异质畸变。这种不稳定性模式通常呈现稀疏性，且无法预先得知哪些特定参数正在发生转变。然而，在功能语境中，这些转变往往是“局部化”的，难点在于参数空间的高维性——单个分量的信噪比可能较低，因此需要跨维度聚合信息以检测全局变化。本文从贝叶斯视角解决功能时间序列中的结构转变检测问题，开发了多种新颖方法，可分别及同时捕捉随机函数序列中固有的结构畸变，问题的构建基于功能时间序列的状态空间表示，并提出了高效的分块吉布斯采样算法以准确识别这些转变位置。此外，我们在多个金融数据集和温度数据集上验证了所提方法的有效性。
英文摘要
In the era of modern data science, the rapid proliferation of high-dimensional and functional datasets has fostered increasing interest in the investigation of paradigm shifts and structural breaks. Unlike classical univariate time series, structural changes in functional data need not occur simultaneously across the entire domain; instead, they may emerge locally, producing heterogeneous distortions across the underlying functional structure. The patterns of instability often exhibit sparsity, where it is not known \textit{a priori} which specific parameters are undergoing a transition. However, in functional contexts, these shifts are often "localised". The difficulty lies in the high dimensionality of the parameter space, where the signal-to-noise ratio may be low for individual components, necessitating the aggregation of information across dimensions to detect a global change. This paper addresses the problem of detecting structural shifts in a functional time series from a Bayesian perspective. We have developed various novel methodologies that capture the inherent structural distortion in a sequence of random functions, both individually and simultaneously. The formulation of the problem is based on the state-space representation of a functional time series. Efficient Blocked Gibbs Sampling algorithms have been proposed to identify these locations accurately. Further, we demonstrate the effectiveness of our methods on several financial and temperature datasets.
