Matrix-variate Smooth Transition Models for Temporal Networks

In many fields, network analysis is used to investigate complex relationships. The increased availability of temporal network data opens the way to the statistical analysis of the network topology and its dynamics. In addition network data are subject to measurement errors and random fluctuations. This calls for realistic time series models which account for relevant features of the data. In this chapter, we propose a new modeling and inference framework for studying matrix-valued panel data characterized by nonlinear dynamics and heavy tails. We assume a smooth transition model for the dynamics and a matrix-variate t distribution for the error term and show how the model can be used in temporal network analysis. Some properties of the model including the close-form expression for the predictor are given. We adopt a Bayesian approach to inference and design an efficient Markov chain Monte Carlo algorithm for approximating the posterior distribution. We apply the proposed model to a volatility network among European firms and an international oil production network and show its ability to account for structural changes. Our framework is motivated by temporal network data, nevertheless, it is general and can be of interest to all researchers interested in the analysis of matrix-variate time series.