Conditionally specified graphical modeling of stationary multivariate time series
平稳多变量时间序列的条件指定图模型AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要直接建立平稳多变量时间序列模型并研究过程依赖和混合性质；图节点是序列，未明确涉及微观网络干扰。
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平稳多变量时间序列的条件指定图模型
- 研究问题
- 对于非高斯或混合结局的多变量时间序列，如何通过条件分布建立有效的平稳联合模型，并用参数表达整个过程的条件独立关系？
- 方法与思路
- 作者为各单变量分量指定指数族条件分布，以过程层面的兼容性构造联合模型，并借助交互核算子的谱性质分析图结构。
- 材料陈述的贡献
- 摘要称建立局部和全局马尔可夫性质，证明模型具有几何混合性，并开发近似 Gibbs 采样器以模拟该平稳图模型的样本路径。
- 阅读关注点
- 应核对条件分布兼容性的具体限制、交互核与边的对应关系，以及平稳性和混合性证明条件、近似采样误差的处理。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或期刊接收；摘要未给出参数估计方案，条件依赖图也不自动具有因果含义。
原文摘要
Graphical models are ubiquitous for summarizing conditional relations in multivariate data. In many applications involving multivariate time series, it is of interest to learn an interaction graph that treats each individual time series as nodes of the graph, with the presence of an edge between two nodes signifying conditional dependence given the others. Typically, the partial covariance is used as a measure of conditional dependence. However, in many applications, the outcomes may not be Gaussian and/or could be a mixture of different outcomes. For such time series using the partial covariance as a measure of conditional dependence may be restrictive. In this article, we propose a broad class of time series models which are specifically designed to succinctly encode process-wide conditional independence in its parameters. For each univariate component in the time series, we model its conditional distribution with a distribution from the exponential family. We develop a notion of process-wide compatibility under which such conditional specifications can be stitched together to form a well-defined strictly stationary multivariate time series. We call this construction a conditionally exponential stationary graphical model (CEStGM). A central quantity underlying CEStGM is a positive kernel which we call the interaction kernel. Spectral properties of such positive kernel operators constitute a core technical foundation of this work. We establish process-wide local and global Markov properties of CEStGM exploiting a Hammersley-Clifford type decomposition of the interaction kernel. Further, we study various probabilistic properties of CEStGM and show that it is geometrically mixing. An approximate Gibbs sampler is also developed to simulate sample paths of CEStGM.