Graphical models for nonstationary time series
Graphical models for nonstationary time series
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DOI：
10.1214/22-aos2205
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发表时间：
2021-09
期刊：
影响因子：
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通讯作者：
Sumanta Basu;S. Rao
中科院分区：
文献类型：
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作者：
Sumanta Basu;S. Rao
我们提出了 NonStGM，一种通用的非参数图形建模框架，用于研究非平稳多元时间序列组成部分之间的动态关联。它建立在高斯图模型（GGM）和平稳时间序列高斯图模型（StGM）的框架之上，并补充了基于变点向量自回归（VAR）的参数图模型的现有工作。与 StGM 类似，所提出的框架以无向图的形式捕获条件非相关性（跨期和同期）。此外，为了描述时间序列组成部分之间更细微的非平稳关系，我们引入了条件非平稳/平稳的新概念，并将其合并到图架构中。这允许人们区分系统组件之间的直接和间接非平稳关系，并且可以用于搜索充当大系统中非平稳性“源”的小子网络。条件非相关性和非平稳性/平稳性这两个概念共同提供了时间序列依赖性结构的简洁描述。
We propose NonStGM, a general nonparametric graphical modeling framework for studying dynamic associations among the components of a nonstationary multivariate time series. It builds on the framework of Gaussian Graphical Models (GGM) and stationary time series Gaussian Graphical model (StGM), and complements existing works on parametric graphical models based on change point vector autoregressions (VAR). Analogous to StGM, the proposed framework captures conditional noncorrelations (both intertemporal and contemporaneous) in the form of an undirected graph. In addition, to describe the more nuanced nonstationary relationships among the components of the time series, we introduce the new notion of conditional nonstationarity/stationarity and incorporate it within the graph architecture. This allows one to distinguish between direct and indirect nonstationary relationships among system components, and can be used to search for small subnetworks that serve as the"source"of nonstationarity in a large system. Together, the two concepts of conditional noncorrelation and nonstationarity/stationarity provide a parsimonious description of the dependence structure of the time series.