Graphical models for nonstationary time series

TL;DR

This paper introduces NonStGM, a nonparametric graphical modeling framework for nonstationary multivariate time series that captures dynamic relationships and distinguishes sources of nonstationarity within the system.

Contribution

It extends Gaussian Graphical Models to nonstationary data by incorporating conditional nonstationarity, enabling detailed analysis of dynamic dependencies and sources of nonstationarity.

Findings

Framework captures both intertemporal and contemporaneous noncorrelations.

Introduces the concept of conditional nonstationarity within graph models.

Facilitates identification of subnetworks responsible for nonstationarity.

Abstract

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.