A0761
Title: Graphical models for nonstationary time series
Authors: Sumanta Basu - Cornell University (United States) [presenting]
Suhasini Subbarao - Texas A&M (United States)
Abstract: NonStGM is proposed, a general nonparametric graphical modelling framework for studying dynamic associations among nonstationary multivariate time series components. It builds on the framework of Gaussian Graphical Models (GGM) and stationary time series Graphical models (StGM). It 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, the new notion of conditional nonstationarity/stationarity is introduced and incorporated within the graph. This can be used to search for small subnetworks that serve as the source of nonstationarity in a large system. Conditional noncorrelation and stationarity between and within the multivariate time series components to zero and Toeplitz embeddings of an infinite-dimensional inverse covariance operator are explicitly connected. 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. It is shown that these sparsity patterns can be recovered from finite-length time series by node-wise regression of discrete Fourier Transforms (DFT) across different Fourier frequencies. The feasibility of learning the NonStGM structure from data using simulation studies is demonstrated.
