We propose NonStGGM, 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 (StGGM), and complements existing works on parametric graphical models based on change point vector autoregressions (VAR). Analogous to StGGM, 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.
翻译:我们提议采用非StGGM,这是一个用于研究非静止多变时间序列各组成部分之间动态联系的一般非参数图形模型框架,它以Gaussian图形模型(GGM)和固定时间序列(StGGM)的框架为基础,并补充基于改变点矢量自动反射(VAR)的参数图形模型的现有工作。对StGGM的模拟,拟议的框架以非方向图形的形式,捕捉有条件的非协调(时际和时际)关系。此外,为了描述时间序列各组成部分之间更为微妙的非静态关系,我们引入了条件性非静止/静态新概念,并将其纳入图形结构。这样可以区分系统各组成部分之间的直接和间接非静止关系,并可用于搜索大系统中作为不静止“源”的小型子网络。同时,两个条件性非同步和非静止/静态概念提供了对时间序列依赖性的描述。