State-Space Modeling of Time-Varying Spillovers on Networks

TL;DR

This paper introduces a novel network state-space modeling framework that captures time-varying spillovers and interactions on networks, providing an interpretable and flexible approach for analyzing complex network time series.

Contribution

The paper develops a new class of network state-space models with stochastic time-varying parameters constrained by known network structures, unifying various existing models and enabling better interpretability.

Findings

The models ensure well-defined second moments despite nonstationarity.

Network versions of stability and local stationarity are established.

The framework allows for shrinkage, thresholding, and low-rank tensor structures.

Abstract

Many modern time series arise on networks, where each component is attached to a node and interactions follow observed edges. Classical time-varying parameter VARs (TVP-VARs) treat all series symmetrically and ignore this structure, while network autoregressive models exploit a given graph but usually impose constant parameters and stationarity. We develop network state-space models in which a low-dimensional latent state controls time-varying network spillovers, own-lag persistence and nodal covariate effects. A key special case is a network time-varying parameter VAR (NTVP-VAR) that constrains each lag matrix to be a linear combination of known network operators, such as a row-normalised adjacency and the identity, and lets the associated coefficients evolve stochastically in time. The framework nests Gaussian and Poisson network autoregressions, network ARIMA models with graph differencing, and dynamic edge models driven by multivariate logistic regression. We give conditions ensuring that NTVP-VARs are well-defined in second moments despite nonstationary states, describe network versions of stability and local stationarity, and discuss shrinkage, thresholding and low-rank tensor structures for high-dimensional graphs. Conceptually, network state-space models separate where interactions may occur (the graph) from how strong they are at each time (the latent state), providing an interpretable alternative to both unstructured TVP-VARs and existing network time-series models.