GRAPHICAL MODELS FOR NONSTATIONARY TIME SERIES

• 成果类型: Article
• 署名作者: Basu, Sumanta; Rao, Suhasini Subba
• 署名单位: Cornell University; Texas A&M University System; Texas A&M University College Station
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2205
• 发表日期: 2023
• 页码: 1453-1483
• 关键词: spectral-analysis; 2nd-order stationarity; covariance; selection; approximation; shrinkage; inference

摘要

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 graphical models (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. This can be used to search for small subnetworks that serve as the source of nonstationarity in a large system. We explicitly connect conditional noncorrelation and stationarity between and within components of the multivariate time series to zero and Toeplitz embeddings of an infinite-dimensional inverse covariance operator. In the Fourier domain, conditional stationarity and noncorrelation relationships in the inverse covariance operator are encoded with a specific sparsity structure of its integral kernel operator. We show that these sparsity patterns can be recovered from finite-length time series by nodewise regression of discrete Fourier transforms (DFT) across different Fourier frequencies. We demonstrate the feasibility of learning NonStGM structure from data using simulation studies.