Estimating Time-Varying Networks With a State-Space Model

Abstract

We propose the use of state-space models (SSMs) to estimate dynamic spatial relationships from time series data. At each time step, the weight matrix, capturing the latent state, is updated by a spatial autoregressive model. Specifically, we consider two types of SSM: the first one calibrates the spatial model to a multivariate regression, while the second one updates the spatial matrix by leveraging the maximum likelihood (ML) estimation. Different filtering algorithms are proposed to estimate the state. The simulation results show that the first model performs robustly for all cases, while the performance of the second model is sensitive to the state dimension. In a real-world case study, we estimate the time-varying weight matrices with weekly credit default swap (CDS) data for 16 banks, and show that the methods can identify communities which are coherent with the country-driven partitions.